Tien Duc Cao
email: tien-duc.cao@inria.fr

Ioana Manolescu
email: ioana.manolescu@inria.fr

Xavier Tannier
email: xavier.tannier@sorbonne-universite.fr

Extracting Linked Data from statistic spreadsheets

Fact-checking journalists typically check the accuracy of a claim against some trusted data source. Statistic databases such as those compiled by state agencies are often used as trusted data sources, as they contain valuable, high-quality information. However, their usability is limited when they are shared in a format such as HTML or spreadsheets: this makes it hard to find the most relevant dataset for checking a specific claim, or to quickly extract from a dataset the best answer to a given query.

In this work, we provide a conceptual model for the open data comprised in statistics published by INSEE, the national French economic and societal statistics institute. Then, we describe a novel method for extracting RDF Linked Open Data, to populate an instance of this model. We used our method to produce RDF data out of 20k+ Excel spreadsheets, and our validation indicates a 91% rate of successful extraction.

Further, we also present a novel algorithm enabling the exploitation of such statistic tables, by (i) identifying the statistic datasets most relevant for a given fact-checking query, and (ii) extracting from each dataset the best specific (precise) query answer it may contain. We have implemented our approach and experimented on the complete corpus of statistics obtained from INSEE, the French national statistic institute.

Our experiments and comparisons demonstrate the effectiveness of our proposed method.

INTRODUCTION

The tremendous value of Big Data has been noticed of late also by the media, and the term "data journalism" has been coined to refer to journalistic work inspired by data sources [START_REF] Gray | The Data Journalism Handbook: How Journalists can Use Data to Improve the News[END_REF]. While data of some form is a natural ingredient of all reporting, the increasing volumes of available digital data as well as its increasing complexity lead to a qualitative jump, where technical skills for working with data are stringently needed in journalism teams.

A class of data sources of particularly high value is that comprised into government statistics. Such data has been painstakingly collected by state administrations which sometimes have very significant human and technology means at their disposal. This makes the data oftentimes of high quality. Another important quality of such data is that it logically falls into the open data category, since it is paid for with taxpayer money. Example of such government open data portals http://data.gov (US), http://data.gov.uk (UK), http://data.gouv.fr and http://insee.fr (France), http://wsl.iiitb.ac.in/sandesh-web/sandesh/index (India) etc.

Such high-quality statistic data is a very good background information to be used when trying to assess the truthfulness of a claim. A fact-checking scenario typically has several steps: first, a claim is made. Second, journalists or other fact-checkers look up reference sources providing relevant statistics for the assessment of the claim; Third, some post-processing may be applied to compute from the reference source values, the value corresponding to the claim. This post-processing may involve elaborate steps.

Ideally, these are available to fact-checkers in a format and organized according to a model that they understand well. For instance, in [START_REF] Wu | Toward Computational Fact-Checking[END_REF], unemployment data is assumed available in a temporal database relation. In reality, however, most fact-checking actors only have access to the data through publication by the institute. This raises the question of the format and organization of the data. While the W3C's best practices argue for the usage of RDF in publishing open data [START_REF]Best Practices for Publishing Linked Data[END_REF], in practice open data may be published Excel, HTML or PDF; in the latter formats, statistic data is typically shown as tables or charts. In the particular case of the INSEE (http://www.insee.fr), the national French social and economic statistics institute, while searching for some hot topics in the current French political debate (youth unemployment, immigrant population etc.) we found many very useful datasets in Excel and/or HTML, sometimes accompanied by a PDF report explaining and commenting the data, but we did not find the data in a structured, machine-readable format.

Motivated by this limitation, we propose an approach for extracting Linked Open Data from INSEE Excel tables. The two main contributions of our work are: (i) a conceptual data model (and concrete RDF implementation) for statistic data such as published by INSEE and other similar institutions, and (ii) an extraction algorithm which populates this model based on about 11,000 pages including 20,743 Excel files published by INSEE. We applied our approach to the complete set of statistics published by INSEE, a leading French national statistics institute, and republish the resulting RDF Open Data (together with the crawling code and the extraction code 1 ). While our approach is tailored to some extent toward French, its core elements are easily applicable to another setting, in particular for statistic databases using English, as the latter is very well-supported by text processing tools.

Subsequently, we develop a system to search for answers to keyword queries in a database of statistics, organized in RDF graphs such as those we produced. Thus, the focus of this system is: given a claim, identify from a corpus of statistics made available as tabular (Excel) files, the information most likely to be useful as background against which to fact-check the claim. Given the variety of data sources and the natural-language nature of a claim, we view this as a top-k search problem, and aim at presenting to the user scored results, in the decreasing order of their matching the claim. We have worked in particular on INSEE data sources, however from our observations, a similar approach can be mapped out to exploit other organizations' statistic databases, such as the ones available at http://www.data.gov or https://data.gov.uk. First, we describe a dataset search algorithm, which given a set of user keywords, identifies the datasets (statistic table and surrounding presentations) most likely to be useful for answering the query. Second, we devised an answer search algorithm which, building on the above algorithm, attempts to answer queries, such as "unemployment rate in Paris in 2016", with values extracted from the statistics dataset, together with a contextualization quickly enabling the user to visually check the correctness of the extraction and the result relevance. In some cases, there is no single number known in the database, but several semantically close ones. In such cases, our algorithm returns the set of numbers, again together with context enabling its interpretation.

We have experimentally evaluated the efficiency and the effectiveness of our algorithms, and demonstrate their practical interest to facilitate fact-checking work. In particular, while political debates are broadcast live on radio or TV, fact-checkers can use such tools to quickly locate reference numbers which may help them publish live fact-checking material.

Below, we describe the data sources we work with and the model for the extracted data (Section 2) and our extraction method (Section 3). We define the search problem that we address in Section 4 and then describe our search algorithms. In Section 5 we present our experimental evaluation. We discuss related work in Section 6, then conclude.

REFERENCE STATISTIC DATA

INSEE data sources INSEE publishes a variety of datasets in many different formats. In particular, we performed a crawl of the INSEE web site under the categories Data/Key figures, Data/Detailed figures, Data/Databases, and Publications/Wide-audience publications, which has lead to about 11,000 web pages including 20,743 Excel files (with total size of 36GB) and 20,116 HTML tables. In this work, we focused on the set of Excel files; we believe our techniques could be quite easily adapted to HTML tables in the future. Also, while we targeted INSEE in this work, we found similar-structure files published in other Open Data government servers in the UK (e.g., http://www.ic.nhs.uk/catalogue/PUB08694/ifs-uk-2010-chap1-tab.xls) and the US (e.g., http://www.eia.gov/totalenergy/data/monthly/query/mer_data_ excel.asp?table=T02.01).

We view each spreadsheet file as a collection of data sheets D 1 , D 2 , . . . Each data sheet D has a title D.t and optionally an outline D.o. The title and outline are given by the statisticians producing the spreadsheets in order to facilitate their understanding by human users, such as the media and general public. The title is a short nominal phrase stating what D contains, e.g., "Average mothers' age at the birth of their child per department in 2015". The outline, when present, is a short paragraph which may be found on a Web page from where the file enclosing D can be downloaded. The outline extends the title, for instance to state that the mothers' ages are rounded to the closest smaller integers, that only the births of live (not stillborn) children are accounted for etc.

In a majority of cases (about two thirds in our estimation), each data sheet D comprises one statistics table, which is typically a two-dimensional aggregate table. Data is aggregated since statistics institutes such as INSEE are concerned with building such global measures of society or economy phenomena, and the aggregate tends to be bidimensional since they are meant to be laid out in a format easy for humans to read. For instance, Figure 1 illustrates a data sheet for the birth statistic dataset mentioned above. In this example, the two dimensions are the mother's age interval, e.g., "16-20", "21-25", "26-30" etc. and her geographic area, specified as a department, e.g., "Essonne", "Val-de-Marne" etc. For a given age interval and region, the table includes the number of women which were first-time mothers in France in 2015, in that age interval and department. In Figure 1, we have included a top row and column on a gray background, in order to refer to the row and column numbers of the cells in the sheet. We will use the shorthand D r,c to denote the cell at row r and column c in D. We see that the table contains data cells, such as D 6,3 , D 6,4 , which hold data values, etc. and header cells, e.g., "Region", "Age below 30" etc., which (i) characterize (provide context for) the data values, and (ii) may occupy several cells in the spreadsheet, as is the case of the latter.

The basic kind of two-dimensional agregate in a data sheet is (close to) the result of a group-by query, as illustrated in Figure 1. However, we also found cases where the data sheet contains a data cube [START_REF] Gray | Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals[END_REF], that is: the result of a group-by, enhanced with partial sums along some of the group-by dimensions. For instance, in the above example, the table may contain a row for every region labeled "Region total" which sums up the numbers for all departments of the region, for each age interval (e.g., https://www.insee.fr/fr/statistiques/fichier/ 2383936/ARA_CD_2016_action_sociale_1-Population_selon_l_age.xls).

Dimension hierarchies are often present in the data. For instance, the dimension values "16-20", "21-25", "26-30" are shown in Figure 1 as subdivisions of "Age below 30", while the next four intervals may be presented as part of "Age above 31". The age dimension hierarchy is shown in magenta in Figure 1, while the geographical dimension hierarchy is shown in blue. In those cases, the lowergranularity dimension values appear in the table close close to the finer-granularity dimension values which they aggregate, as exemplified in Figure 1. Cell fusion is used in this case to give a visual cue of the finer-granularity dimension values corresponding to the lower-granularity dimension value which aggregates them.

A few more rules govern data organization in the spreadsheet: (1) D 1,1 (and in some cases, more cells on row 1, or the first few rows of D) contain the outline D.o, as illustrated in Figure 1; here, the outline is a long text, thus a spreadsheet editor would show it over several cells. One or several fully empty rows separate the outline from the topmost cells of the data table; in our example, this is the case of row 2. Observe that due to the way data is spatially laid out in the sheet, these topmost cells are related to the lowest granularity (top of the hierarchy) of one dimension of the aggregate. For instance, in Figure 1, this concerns the cell at line 3 and columns 3 to 9, containing Mother's age at the time of the birth.

(2) Sometimes, the content of a header cell (that is, a value of an aggregation dimension) is not human-understandable, but it is the name of a variable or measure, consistently used in all INSEE publications to refer to a given concept. Exactly in these cases, the file containing D has a sheet immediately after D, where the variable (or measure) name is mapped to the natural-language description explaining its meaning. aggregations over the values of other data cells. Thus, our current extraction algorithm (described below) would extract data from such cubes as if they were result of a plain aggregation query. This clearly introduces some loss of information; we are working to improve it in a future version.

EXTRACTION

We developed a tool for extracting data from spreadsheet files so as to populate an instance of our conceptual data model; it uses the Python library xlrd (https://pypi.python.org/pypi/xlrd) for accessing spreadsheet content. Below, we present the extraction procedure. Unlike related work (see Section 6), it is not based on a sequence classification with a supervised learning approach, but on a more global rule-based system aiming at framing the data cell range and extracting the headers around these data cell.

For each sheet, the first task is to identify the data cells. In our corpus, these cells contain numeric information, that is: integers or real numbers, but also interval specifications such as "20+" (standing for "at least 20"), special null tokens such as "n.s." for "not specified".

Our approach is to identify the rectangular area containing the main table (of data cells), then build data cells out of the (row, column) locations found in this area. Note that the area may also contain empty locations, corresponding to the real-life situation when an information is not available or for some reason not reported, as is the case for D 9,9 in Figure 1.

Data cell identification proceeds in several steps. DCI1 Identify the leftmost data location (ldl) on each row: this is the first location encountered from left to right which (i) follows at least one location containing text (such locations will be interpreted as being part of header cells), and (ii) has a non-empty content that is compatible with a data cell (as specified above). We store the column numbers of all such leftmost data locations in an array called ldl; for instance, ldl [START_REF] Ahsan | Towards Spreadsheet Integration Using Entity Identification Driven by a Spatial-temporal Model[END_REF] = -1 (no data cell detected on row 1) and the same holds for rows 2 to 5, while ldl[i] = 3 for i = 6, 7 etc. DCI2 For each row i where ldl[i] -1, we compute a row signature si [i] which is counts the non-empty locations of various types found on the row. For instance, si [6] = {strin : 2, num : 7} because the row has 2 string-valued cells ("Île-de-France" and "Essonne") and 7 numerical cells. For each signature thus obtained, we count the number of rows (with data cells) having exactly that signature; the largest row set is termed the data table seed. Note that the rows in the data table seed are not necessarily contiguous. This reflects the observation that slightly different-structured rows are sometimes found within the data table; for instance, D 9,9 is empty, therefore row 9 is not part of the seed, which in this example, consists of the rows {6,7,8,10,11} and possibly other rows (not shown) below. DCI3 We "grow" the data table seed it by adding every row at distance 1 or at most 2 above and below the data table seed, and which contains at least a data cell. We do this repeatedly until no such rows can be found. In our example, this process adds row 9, despite the fact that it does not have the same signature as the others. We repeat this step in an inflationary fashion until no row adjacent to the current data table qualifies. The goal of this stage is to make sure we do not miss interesting data cells by being overly strict w.r.t. the structure of the rows containing data cells.

At this point, all the data cells are known, and their values and coordinates can be extracted.

Identification and extraction of header cells

We first look for those organized in rows, e.g., rows 3, 4 and 5 in our example. HCE1 We attempt to exploit the visual layout of the file, by looking for a horizontal border which separates the first header row of the (usually empty) row above it. HCE1.1 When such a border exists (which represents a majority but not all the cases), it is a good indicator that header cells are to be found in the rows between the border and going down until (and before) the first data row. (Note that the data rows are already known by now.) In our example, this corresponds to the rectangular area whose corners are D 3,1 and D 4,9 . HCE1.2 When the border does not exist, we inspect the rows starting immediately above the first data row and moving up, as follows. In each row i, we examine the locations starting at the column ldl[i] (if this is greater than 0). If the row doesn't contain empty locations, we consider that it is part of the header area. Intuitively, this is because no data cell can lack a value along one of the dimensions, and header cells carry exactly dimension values. An empty header cell would correspond precisely to such a missing dimension value. HCE2 Once the header area is known, we look for conceptual header cells. The task is complicated by the fact that such a cell may be spread over several locations: typically, a short text is spread from the top to the bottom over locations situated one on top of the other. This can also happen between locations in the same row (not in the same column), which are fused: this is the case of D 3,3 to D 3,9 in our example. The locations holding a single dimension value are sometimes (but not always) fused in the spreadsheet; sometimes, empty locations are enclosed within the same border as some locations holding text, to obtain a visually pleasing aspect where the dimension value "stands out well". We detect such groups by tracking visible cell borders, and create one conceptual header cell out of each area border-enclosed area. HCE3 Next, we identify and extract header cells organized in columns, e.g., columns 1 and 2 in our example. This is done by traversing all the data rows in the data area, and collecting from each row i, the cells that are at the left of the leftmost data cell ldl[i].

Finally, we populate the instance of the data model with the remaining relationships we need. We connect: each data and header cell to its respective locations; each data cell with its closest header cell on the same column, and with its closest header cell on the same row; each row (respectively, column) header cell to its closest header cell above (respectively, at left) through the relation aggregated by.

SEARCH PROBLEM AND ALGORITHM

Given a keyword-based query, we focus on returning a ranked list of candidate answers, ordered in the decreasing likelihood that they contain (or can be used to compute) the query result. A relevant candidate answer can be a data cell, a data row, column or even an entire dataset. For example, consider the query "youth unemployment in France in August 2017". An Eurostat dataset2 is a good candidate answer to this query, since, as shown in Figure 3, it contains one data cell, at the intersection of the France row with the Aug-2017 column. Now, if one changes the query to ask for "youth unemployment in France in 2017", no single data cell can be returned; instead, all the cells on the France row qualify. Finally, a dataset containing 2017 French unemployment statistics over the general population (not just youth) meets some of the search criteria (2017, France, unemployment) and thus may deserve to appear in the ranked list of results, depending on the availability of better results.

This task requires the development of specific novel methods, borrowing ideas from traditional IR, but following a new methodology. This is because our task is very specific: we are searching for information not within text, but within tables, which moreover are not flat, first normal form database relations (for which many keyword search algorithms have been proposed since [START_REF] Hristidis | DISCOVER: Keyword Search in Relational Databases[END_REF]), but partially nested tables, in particular due to the hierarchical nature of the headers, as we explained previously. While most of the reasoning performed by our algorithm follows the two-dimensional layout of data in columns and tables, bringing the data in RDF: (i) puts a set of interesting, high-value data sources within reach of developers and (ii) allows us to query across nested headers using regular path queries expressed in SPARQL (as we explain in Section 4.6).

We describe our algorithms for finding such answers below.

Input data and architecture

System architecture A scraper collects the Web pages publicly accessible from a statistic institute Web site; Excel and HTML tables are identified, traversed, and converted into RDF graphs as explained above. The resulting RDF data is stored in the Apache Jena TDB server 3 , and used to answer keyword queries as we explain next. A dataset consists of header cells and data cells. Data cells and header cells each have attributes indicating their position (column and row) and their value. For instance, in Figure 3, "Belgium", "Bulgaria" etc. up to "France", "Oct-2016" to "Oct-2017", and the two fused cells above them, are header cells, while the other are data cells. Each data cell has a closest header cell on its column, and another one on its row; these capture the dimension values corresponding to a data cell.

To enable linking the results with existing (RDF) datasets and ontologies, we extract the table contents into an RDF graph. We create an RDF class for each entity type, and assign an URI to each entity instance, e.g., dataset, table, cell, outline etc. Each relationship is similarly represented by a resource described by the entity instances participating to the relationship, together with their respective roles.

Dataset search

The first problem we consider is: given a keyword query Q consisting of a set of keywords u 1 , u 2 , . . ., u m and an integer k, find the k datasets most relevant for the query (we explain how we evaluate this relevance below).

We view each dataset as a table containing a title, possibly a comment, a set of header cells (row header cells and column header 3 https://jena.apache.org/documentation/tdb/index.html cells) and a set of data cells, the latter containing numeric data 4 . At query time, we transform the query Q into a set of of keywords W = w 1 ,w 2 , . . . ,w n using the method described in Section 4.3. Offline, this method is also used to transform each dataset's text to words and we compute the score of each word with respect to a dataset, as described in Section 4.4. Then, based on the word-dataset score and W , we estimate datasets' relevance to the query as we explain in Section 4.5.

Text processing

Given a text t (appearing in a title, comment, or header cell of the dataset, or the text consisting of the set of words in the query Q), we convert it into a set of words using the following process:

• First, t is tokenized (separated into distinct words) using the KEA 5 tokenizers. Subsequently, each multi-word French location found in t that is listed in Geonames 6 , is put together in a single token. • Each token (word) is converted to lowercase, stop words are removed, as well as French accents which complicate matching. • Each word is mapped into a word2vec vector [START_REF] Mikolov | Distributed Representations of Words and Phrases and their Compositionality[END_REF], using the gensim [START_REF] Radim | Software Framework for Topic Modelling with Large Corpora[END_REF] tool. Bigrams and trigrams are considered following [START_REF] Mikolov | Distributed Representations of Words and Phrases and their Compositionality[END_REF]. We had trained the word2vec model on a general-domain French news web page corpus.

Word-dataset score

For each dataset extracted from the statistic database, we compute a score characterizing its semantic content. A first observation is that datasets should be returned not only when they contain the exact words present in the query, but also if they contain very closely related ones. For example, a dataset titled "Duration of marriage" could be a good match for the query "Average time between marriage and divorce" because of the similarity between "duration" and "time". To this effect, we rely on word2vec [START_REF] Mikolov | Distributed Representations of Words and Phrases and their Compositionality[END_REF] which provides similar words for any word in its vocabulary: if a word w appears in a dataset D, and w is similar to w , we consider w also appears in D.

The score score (w ) of a dataset D w.r.t the query word w is 1 if w appears in D.

If w does not appear in D:

• If there exists a word w , from the list of top-50 similar words of w according to word2vec, which appears in D, then score (w ) is the similarity between w and w . If there are several such w , we consider the one most similar to w. • If w is the name of a Geonames place we can't apply the above scoring approach because "comparable" places (e.g., cities such as Paris and London) will have high similarity in the word2vec space. As the result, when user asks for "unemployment rate Paris", the data of London might be returned instead of Paris's. Let p be the number of places that Geonames' hierarchy API 7 returns for w (p is determined by Geonames and depends on w). For instance, when querying the API with Paris, we obtain the list Île-de-France, France, Europe. Let w i be the place at position i, 1 ≤ i ≤ p in this list of returned places, such that w i appears in D.

Then, we assign to D a score for w equal to (p +1-i)/(p +1), that is, the most similar place according to Geonames has rank p/(p + 1), and the least similar has the rank 1/(p + 1).

If D contains several of the places from the w's hierarchy, we assign to D a score for w corresponding to the highestranked such place. • 0 otherwise.

Based on the notion of word similarity defined above, we will write w ≺ W to denote that the word w from dataset D either belongs to the query set W , or is close to a word in W . Observe that, by definition, for any w ≺ W , we have score (w ) > 0.

We also keep track of the location(s) (title, header and/or comment) in which a word appears in a dataset; this information will be used when answering queries, as described in Section 4.5. In summary, for each dataset D and word w ∈ D such that w ≺ W , we compute and store tuples of the form: We experimented with many score functions that give high ranking to datasets that have many matching keywords (see details in section 5.2.2). These functions are monotonous in the score of D with respect to each individual word w. This enables us to apply Fagin's threshold algorithm [START_REF] Fagin | Optimal Aggregation Algorithms for Middleware[END_REF] to efficiently determine the k datasets having the highest 1 score for the query W .

Location-aware score components The location -title (T), row or column headers (HR or HC), or comments (C) -where a keyword occurs in a dataset can also be used to assess the dataset relevance. For example, a keyword appearing in the title often signals a dataset more relevant for the search than if the keyword appears in a comment. We exploit this observation to pre-filter the datasets for which we compute exact scores, as follows.

We run the TA algorithm using the score function 1 to select r × k datasets, where r is an integer larger than 1. For each dataset thus retrieved, we compute a second, refined score function 2 (see below), which also accounts for the locations in which keywords appear in the datasets; the answer to the query will consists of the top-k datasets according to 2 .

The second score function 2 (D,W ) is computed as follows. Let w be a word appearing at a location loc ∈ {T, HR, HC, C} such that w ≺ W . We denote by w loc, D (or just w loc when D is clear from the context) the existence of one or several located occurrence of w in D in loc. Thus, for instance, if "youth" appears twice in the title of D and once in a row header, this leads to two located occurrences, namely youth T, D and youth HR, D .

Then, for loc ∈ {T, HR, HC, C} we introduce a coefficient α loc allowing us to calibrate the weight (importance) of keyword occurrences in location loc. To quantify D's relevance for W due to its loc occurrences, we define a location score component f loc (D,W ). In particular, we have experimented with two f loc functions:

• f sum loc (D,W ) = α w ≺W scor e (w l oc, D ) loc • f count loc (D,W ) = α count {w ≺W } loc
where for score (w loc, D ) we use the value score (w ), the score of D with respect to w (Section 4.4). Thus, each f loc "boosts" the relevance scores of all loc occurrences by a certain exponential formula, whose relative importance is controlled by α loc .

Further, the relevance of a dataset increases if different query keywords appear in different header locations, that is, some in HR (header rows) and some in HC (header columns). In such cases, the data cells at the intersection of the respective rows and columns may provide very precise answers to the query, as illustrated in Figure 3: here, "France" is present in HC while "youth" and "17" appear in HR.

To reflect this, we introduce another function f H (D,W ) computed on the scores of all unique located occurrences from row or column headers; we also experimented with the two variants, f sum H and f count H introduced above. Putting it all together, we compute the content-and location-aware relevance score of a dataset for W as:

2 (D,W ) = 1 (D,W ) + Σ loc ∈ {T,HR,HC,C} f loc (D,W ) + f H (D,W )
Finally, we also experimented with another function * (D,W ) defined as:

* 2 (D,W ) =      2 (D,W ), if f T (D,W ) > 0 0, otherwise *
2 discards datasets having no relevant keyword in the title. This is due to the observation that statistic dataset titles are typically carefully chosen to describe the dataset; if no query keyword can be connected to it, the dataset is very likely not relevant.

Data cell search

We now consider the problem of identifying the data cell(s) (or the data rows/columns) that can give the most precise answer to the user query.

Such an answer may consist of exactly one data cell. For example, for the query "unemployment rate in Paris", a very good answer would be a data cell D r,c whose closest row header cell contains "unemployment rate" and whose closest column header cell contains "Paris". Alternatively, query keywords may occur not in the closest column header cell of D r,c but in another header cell that is its ancestor in D. For instance, in Figure 3, let D r,c be the data cell at the intersection of the Aug-17 column with the France row: the word "youth" occurs in an ancestor of the Aug-17 header cell, and "youth" clearly characterizes D r,c 's content. We say the closest (row and column) header cells of D r,c and all their ancestor header cells characterize D r,c . Another valid answer to the "unemployment rate in Paris" query would be a whole data row (or a whole column) whose header contains "unemployment" and "Paris". We consider this to be less relevant than a single data cell answer, as it is less precise.

We term data cell answer an answer consisting of either a data cell, or a row or column; below, we describe how we identify such answers.

We identify data cells answers from a given dataset D as follows. Recall that all located occurrences in D, and in particular those of the form w HR and w HC for w ≺ W , have been pre-computed; each such occurrence corresponds either to a header row r or to a header column c. For each data cell D r,c , we define #(r,c) as the number of unique words w ≺ W occurring in the header cells characterizing D r,c . Data cells in D may be characterized by:

(1) Some header cells containing HR occurrences (for some w ≺ W ), and some others containing HC occurrences; (2) Only header cells with HR occurrences (or only header cells with HC ones).

Observe that if D holds both cell answers (case 1) and row-or column answers (case 2), by definition, they occur in different rows and columns. Our returned data cell answers from D are:

• If there are cells in case 1, then each of them is a data cell answer from D, and we return cell(s) with highest #(r ,c) values. • Only if there are no such cells but there are some relevant rows or columns (case 2), we return the one(s) with highest #(r ,c) values. This is motivated by the intuition that if D has a specific, one-cell answer, it is unlikely that D also holds a less specific, yet relevant one.

Concretely, we compute the #(r,c) values based on the (word, score, location, dataset) tuples we extract (Section 4.4). We rely on SPARQL 1.1 [START_REF] W3c | SPARQL Protocol and RDF Query Language[END_REF] queries on the RDF representation of our datasets (Section 4.1) to identify the cell or row/column answer(s) from each D. SPARQL 1.1 features property paths, akin to regular expressions; we use them to identify all the header cells characterizing a given D r,c .

Note that this method yields only one element (cell, row or column) from each dataset D, or several elements if they have the exact same score. An alternative would have been to allow returning several elements from each dataset; then, one needs to decide how to collate (inter-rank) scores of different elements identified in different datasets. We consider that this alternative would increase the complexity of our approach, for unclear benefits: the user experience is often better when results from the same dataset are aggregated together, rather than considered as independent. Suggesting several data cells per dataset is then more a question of result visualization than one pertaining to the search method.

EXPERIMENTAL EVALUATION

We describe here experiments evaluating the quality and the speed of our algorithms. Section 5.1 considers RDF data extraction from spreadsheet data, while Section 5.2 studies query answering.

Extraction

From 20,743 Excel files collected, we selected at random 100 unseen files to evaluate the reliability of the extraction process; these files contained a total of 2432 tables. To avoid very similar files in our evaluation, e.g., tables showing the same metric for distinct years, we required the first three letters in the name of each newly selected file, to be different from the first three letters in the names of all the files previously selected to be included in the test batch.

For these 100 files, we visually identified the header cells, data cells and header hierarchy, which we compared with those obtained from our extractor. We consider a table is "correctly extracted" when all these are pairwise equal; otherwise, the table is "incorrectly extracted". We recorded 91% (or 2214) tables extracted correctly, and 9% (or 218) incorrectly extracted. Most of the incorrect extractions were due to sheets with several tables (not just one). We plan to extend our system to also handle them correctly.

Overall, the extraction produced 2.68 • 10 6 row header cells, 122 • 10 6 column header cells, and 2.24 • 109 data cells; the extraction algorithm ran for 5 hours.

Search algorithm

In this section, we evaluate the quality and speed of our search algorithm. Section 5.2.1 describes the dataset and query workload we used, which was split into a development set (on which we tuned our score functions) and a test set (on which we measured the performance of our algorithms). It also specifies how we built a "gold-standard" set of answers against which our algorithms were evaluated. Section 5.2.2 details the choice of parameters for the score functions.

Datasets and Queries.

We have developed our system in Python (61 classes and 4071 lines). Crawling the INSEE Web site, we extracted information out of 19,984 HTML tables and 91,161 spreadsheets, out of which we built a Linked Open Data corpus of 945 millions RDF triples.

We collected all the articles published online by the fact-checking team "Les Décodeurs",8 a fact-checking and data journalism team of Le Monde, France's leading national newspaper, between March 10th and August 2nd, 2014; there were 3,041 articles. From these, we selected 75 articles whose fact-checks were backed by INSEE data; these all contain links to https://www.insee.fr. By reading these articles and visiting their referenced INSEE dataset, we identified a set of 55 natural language queries which the journalists could have asked a system like ours. 9 We experimented with a total of 288 variants of the 2 function:

• 1 was either 1a , 1b or 1c ;

• 2 relied either on f sum loc or on f count loc ; for each of these, we tried different value combinations for the coefficients α T , α HC , α HR and α C ; • we used either the 2 formula, or its * 2 variant. We built a gold-standard reference to this query set as follows. We ran each query q through our dataset search algorithm for each of the 288 2 functions, asking for k = 20 most relevant datasets. We Figure 4: Screen shot of our search tool. In this example, the second result is a full column; clicking on "Tous les résultats" (all results) renders all the cells from that column.

built the union of all the answers thus obtained for q and assessed the relevance of each dataset as either 0 (not relevant), 1 ("partially relevant" which means user could find some related information to answer their query) or 2 ("highly relevant" which means user could find the exact answer for their query); a Web front-end was built to facilitate this process.

Search experiments.

We specify our evaluation metric, then describe how we tuned the parameters of our score function, and the results of our experiments focused on the quality of the returned results. Last but not least, we put them into the perspective of a comparison with the baselines which existed prior to our work: INSEE's own search system, and plain Google search.

Evaluation Metric

We evaluated the quality of the answers of our runs and of the baseline systems by their mean average precision (MAP 10 ), widely used for evaluating ranked lists of results.

MAP is traditionally defined based on a binary relevance judgment (relevant or irrelevant in our case). We experimented with the two possibilities:

• MAP h is the mean average precision where only highly relevant datasets are considered as relevant • MAP p is the mean average precision where both partially and highly relevant datasets are considered relevant.

Parameter Estimation and Results

We experimented with the following flavors of the 1 function :

• 1b (D,W ) = 10 w ≺W
scor e (w )

• 1d (D,W ) = 10 count {w ≺W } • 1f (D,W ) = w ≺W 10 scor e (w )
We also experimented with some modified variants that take into account the sum of matching keywords:

• 1c (D,W ) = w ≺W score (w ) + 1b (D,W ) • 1e (D,W ) = w ≺W score (w ) + 1d (D,W ) • 1 (D,W ) = w ≺W score (w ) + 1f (D,W )
A randomly selected development set of 29 queries has been used to select the best values for the 7 parameters of our system : α T , α C , α HR , α HC , α H , as well as the different versions of 1 and 2 . For this purpose, we ran a grid search with different values of these parameters, selected among {3,5,7,8,10}, on the development query We found that a same score function has lead to the best MAP h and the best MAP p on the development query set. In terms of the notations introduced in Section 4.5, this best-performing score function is obtained by:

• Using Given that our test query set was relatively small, we performed two more experiments aiming at testing the robustness of the parameter selection on the development set:

• We used a randomly selected subset of 17 queries among the 29 development queries, and used it as a new development set. The best score function for this new development set was the same; further, the MAP results on the two development sets are very similar (see Table 1). • We computed the MAP scores obtained on the full development set for all 288 combinations of parameters, and plotted them from the best to the worst (Figure 5; due to the way we plot the data, two MAP h and MAP p values shown on the same vertical line may not correspond to the same score function). The figure shows that the best-performing 15 combinations leads to scores higher than 0.80, indicating that any of these could be used with pretty good results. These two results tend to show that we can consider our results as stable, despite the relatively small size of the query set.

Running time Processing and indexing the words (close to those) appearing in the datasets took approximately three hours. We ran our experiments on a machine with 126GB RAM and 40 CPUs Intel(R) Xeon(R) E5-2640 v4 @ 2.40GHz. The average query evaluation time over the 55 queries we identified is 0.218 seconds.

Comparison against Baselines To put our results into perspective, we also computed the MAP scores of our test query set on the 11 , and Google search instructed to look only within the INSEE web site. Similarly to the evaluation process of our system, for each query we selected the first 20 elements returned by these systems and manually evaluated each dataset's relevance to the given query. Table 2 depicts the MAP results thus obtained, compared against those of our system. Google's MAP is very close to ours; while our work is obviously not placed as a rival of Google in general, we view this as validating the quality of our results with (much!) smaller computational efforts. Further, our work follows a white-box approach, whereas it is well known that the top results returned by Google are increasingly due to other factors beyond the original PageRank [START_REF] Brin | The Anatomy of a Large-Scale Hypertextual Web Search Engine[END_REF] information, and may vary in time and/or with result personalization, Google's own A/B testing etc.

We end this comparison with two remarks. (i) Our evaluation was made on INSEE data alone due to the institute's extensive database on which fact-checking articles were written, from which we derived our test queries. However, as stated before, our approach could be easily adapted to other statistic Web sites, as we only need the ability to crawl the tables from the Web site. As is the case for INSEE, this method may be more robust than using the category-driven navigation or the search feature built in the Web site publishing the statistic information. (ii) Our system, based on a fine-granularity modeling of the data from statistic tables, is the only one capable of returning cell-level answers (Section 4.6). We show such answers to the users together with the header cells characterizing them, so that users can immediately appreciate their accuracy (as in Figure 4). 11 Available at https://insee.fr 6 RELATED WORK Section 6.1 puts our data extraction work into the perspective of comparable methods. Then, Section 6.2 focuses on answering keyword queries.

Extraction

Closest to our work, [START_REF] Chen | Automatic Web Spreadsheet Data Extraction[END_REF] automatically extracts relational data from spreadsheets. Their system used conditional random fields (CRF) [START_REF] Lafferty | Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data[END_REF] to identify data frames: such a frame is a value region which contains numeric cells, top attributes and left attributes corresponding to header cells and their hierarchies. From a collection of 410,554 Excel files collected from the Web, they selected randomly 100 files, labeled 27,531 non-empty rows (as title, header, data or footnote) manually by human experts, then used this dataset for training and evaluation. They obtained significant better precision and recall metrics when taking into account both textual and layout features for CRF. SVM was applied on header cells to learn about their hierachies. The model achieved a precision of 0.921 for top headers, and 0.852 for left headers. However, these numbers should not be compared with our results, because the datasets are different (tables encountered on the Web vs. government statistics), as well as the evaluation metrics (cell-by-cell assessment in [START_REF] Chen | Automatic Web Spreadsheet Data Extraction[END_REF] vs. binary assessment over the entire sheet extraction in our case). Overall, their method is more involved, whereas our method has the advantage of not requiring manual labeling. We may also experiment with learning-based approaches in the future. [START_REF] Ahsan | Towards Spreadsheet Integration Using Entity Identification Driven by a Spatial-temporal Model[END_REF] describes an extractor to automatically identify in spreadsheets entities like location and time.

Data extraction from tables encoded as HTML lists has been addressed e.g., in [START_REF] Elmeleegy | Harvesting Relational Tables from Lists on the Web[END_REF]. Structured fact extraction from text Web pages has lead to the construction of knowledge bases such as Yago [START_REF] Mahdisoltani | YAGO3: A Knowledge Base from Multilingual Wikipedias[END_REF] and Google's Knowledge Graph [START_REF] Luna | From Data Fusion to Knowledge Fusion[END_REF]. Our work has a related but different focus as we focus on high-value, high-confidence, finegranularity, somehow-structured data such as government-issue statistics; this calls for different technical methods.

In prior work [START_REF] Goasdoué | Fact Checking and Analyzing the Web (demonstration)[END_REF], we devised a tool for exploiting background information (in particular, we used DBPedia RDF data) to add context to a claim to be fact-checked; in this work, we tackle the complementary problem of producing high-value, high-confidence Linked Open Data out of databases of statistics.

While in this work, we focused on improving the usability of statistic tables (HTML tables or spreadsheets) as reference data sources against which claims can be fact-checked, other works focused on building textual reference data source from general claims [START_REF] Bar-Haim | Stance Classification of Context-Dependent Claims[END_REF][START_REF] Levy | Context Dependent Claim Detection[END_REF], congressional debates [START_REF] Thomas | Get out the vote: Determining support or opposition from Congressional floor-debate transcripts[END_REF] or tweets [START_REF] Rajadesingan | Identifying Users with Opposing Opinions in Twitter Debates[END_REF].

Some works focused on exploiting the data in HTML and spreadsheet tables found on the Web. Tschirschnitz et al. [START_REF] Tschirschnitz | Detecting Inclusion Dependencies on Very Many Tables[END_REF] focused on detecting the semantic relations that hold between millions of Web tables, for instance detecting so-called inclusion dependencies (when the values of a column in one table are included in the values of a column in another table).

Search problem

Also seeking to facilitate access to spreadsheet data, M. Kohlhase et al. [START_REF] Kohlhase | XLSearch: A Search Engine for Spreadsheets[END_REF] built a search engine for finding and accessing spreadsheets by their formulae. This is less of an issue for the tables we focus on, as they contain plain numbers and not formulas.

We are not aware of a previous work addressing the same question as ours, namely: finding the tabular dataset, and the data cell answers, most relevant to a given keyword query. Keyword search has been addressed by a vast literature in text and Web documents, as well as for XML documents, e.g. [START_REF] Hristidis | DISCOVER: Keyword Search in Relational Databases[END_REF], relational databases, e.g. [START_REF] Sayyadian | Efficient Keyword Search Across Heterogeneous Relational Databases[END_REF], and RDF graphs, e.g. [START_REF] Elbassuoni | Keyword Search over RDF Graphs[END_REF][START_REF] Le | Scalable Keyword Search on Large RDF Data[END_REF]. Thus, one could apply such an RDF keyword search algorithm to our search problem. However, there are differences: (i) the abovementioned RDF keyword search work do not return datasets, but answer trees, that is: trees that are subgraphs of the RDF graph, such that each tree has one node containing each query keyword. From this perspective, an RDF keyword search algorithm competes with our cell search but not with our dataset search; (ii) more importantly, answer trees to RDF keyword search are ranked according to metrics such as their size (number of edges), and such metrics are agnostic of the particular type and role of each RDF node. In the RDF datasets we work with, data and header cells play very specific roles, which are not taken into account by a generic RDF keyword search algorithm would not. In contrast, our approach ranks datasets, and then data cell answers, by carefully considering all their content (in title, headers, comments) and their spatial placement of such content in the original table, as discussed in Section 4.5 and Section 4.6.

Google's Fusion Tables work [START_REF] Gonzalez | Google Fusion Tables: Data Management, Integration, and Collaboration in the Cloud[END_REF] focuses on storing, querying and visualizing tabular data, however, it does not tackle keyword search with a tabular semantics as we do. Google has also issued Google Tables as a working product 12 . In March 2018, we tried to use it for some sample queries we addressed in this paper, but the results we obtained were of lower quality (some were irrelevant). We believe this may be due to Google's focus on data available on the Web, whereas we focus on very high-quality data curated by INSEE experts, but which needed our work to be easily searchable.

Currently, our software is not capable of aggregating information, e.g., if one asks for unemployed people from all departements within a region, we are not capable of summing these numbers up into the number corresponding to the region. This could be addressed in future work which could focus on applying OLAP-style operations of drill-down or roll-up to further process the information we extract from the INSEE datasets.

Our extraction method was published in [START_REF] Cao | Extracting Linked Data from Statistic Spreadsheets[END_REF], while the query algorithm will be soon presented in [START_REF] Cao | Searching for Truth in a Database of Statistics[END_REF].

CONCLUSION

We have described an ongoing effort to extract Linked Open Data from data tables produced by the INSEE statistics institute, and shared by them under the form of Excel tables. We do this as part of our work in the ContentCheck R&D project 13 , which aims at investigating content management techniques (from databases, knowledge management, natural language processing, information extraction and data mining) to provide tools toward automating and supporting fact-checker journalists' efforts. Computational fact-checking is a very active areas, approached from many perspectives [START_REF] Cazalens | A Content Management Perspective on Fact-Checking[END_REF], [START_REF] Leblay | Computational factchecking: problems, state of the art, and perspectives[END_REF]. In the effort described here, we worked toward enabling trusted statistic data sources to be used as background information, when trying to determine the degree of thruthfulness of a claim.

Our current work aims at automatically identifying mentions of statistics within texts, for instance, in a phrase of the form "Despite many successive public policies, youth unemployment in France is still above 10%", our goal is to automatically identify "youth unemployment above 10%". Combined with the search functionality described in this work, such automatic identification would allow moving one step forward toward automating fact-checking.

Figure 2 :

 2 Figure 2: Conceptual data model.

Figure 3 :

 3 Figure 3: Sample dataset on French youth unemployment.

4 . 5

 45 (w, score (w ), location(w, D), D) where location(w, D) ∈ {T, HR, HC, C} indicates where w appears in D: T denotes the title, HR denotes a row header cell, HC denotes a column header cell, and C denotes an occurrence in a comment. These tuples are encoded in JSON and stored in a set of files; each file contains the scores for one word (or bigram) w, and all the datasets. Relevance score function Content-based relevance score function. This function, denoted 1 (D,W ), quantifies the interest of dataset D for the word set W ; it is computed based on the tuples (w, score (w ), location(w, D), D) where w ≺ W .

  1,c ; • Using f sum and the coefficient values α T = 10, α C = 3, α HR = 5, α HC = 5 and α H = 7; • Using the * 2 variant, which discards datasets lacking matches in the title. On the test set, this function has lead to MAP p = 0.76 and MAP h = 0.70 .

Figure 5 :

 5 Figure 5: MAP results on the development set for 288 variants of the score function.

  For example, we translate SEXE1_AGEPYR1018 . Further, the header cells are organized in an aggregation hierarchy materialized by the respective relation "aggregated by". For instance, D 5,4 is aggregated by D 4,3 , which is agregated by D 3,3 .In each sheet, we identify the top dimension values as those which are not aggregated by any other values: in our example, the top dimension values appear in D 3,3 , D 6,1 and D 9,1 . Note that such top dimension values are sometimes dimensions names, e.

	H l	H H	H c H 1 The data reflects children born alive in 2015... 1 2 3	4	5	6	7	8	9 10
			2
			3				Mother's age at the time of the birth
			4			Age below 30			Age above 31
			5	Region	Department 16-20 21-25 26-30 31-35 36-40 41-45 46-50
			6		Essonne	215 1230 5643 4320 3120 1514	673
			7	Île-de-France	Val-de-Marne	175	987 4325 3156 2989 1740	566
			8		. . .	. . .	. . .	. . .	. . .	. . .	. . .	. . .
			9		Ain	76 1103 3677 2897 1976 1464
			10	Rhône-Alpes	Ardèche	45	954 2865 2761 1752 1653	523
			11		. . .	. . .	. . .	. . .	. . .	. . .	. . .	. . .
		. . .	. . .	. . .	. . .	. . .	. . .	. . .	. . .	. . .	. . .
				Figure 1: Outline of a sample statistics table in an INSEE dataset.
	(https://www.insee.fr/fr/statistiques/fichier/2045005/BTX_TD_POP1A_2013.zip)					aggregated by
	into Male from 18 to 24 years old using the table below:
											Top dim. value (row)
	Variable	Meaning
	SEXE			Sex					Sheet	Header cell	value
	1 2 AGEPYR10 00 03 06 11 . . . 80 Conceptual data model From the above description of the INSEE Male Female Age group Less than 3 years old 3 to 5 years old 6 to 10 years old 11 to 17 years old . . . statistic datasets, we extract a conceptual data model shown in Fig-ure 2. Entities are shown as boxes while attributes apper in oval shapes. We simplified the notation to depict relationships as directed arrows, labeled with the relationship name. Data cells and header cells each have an attribute indicating their value (content); by defi-nition, any data or header cell has a non-empty content. Moreover, a data cell has one associated location, i.e., (row number, column number), while a header cell may occupy one or several (adjacent) locations. Each data cell has a closest header cell on its column, and another one on its line; these capture the dimension values corre-sponding to a data cell. For instance, the closest column header cell for the data cell at D 7,4 is D 5,4 , while the closest column header cell is D 7,2 Data cell name description Dataset source 80 years and older Closest header cell (row) title outline Top dim. value (col) Closest header cell (col) consists of	value row col Location p o s i t i o n p o s i t i o n

g., Region, and other times dimensions values, e.g., Île-de-France. Statistics in a sheet are not always organized exactly as predicted by the relational aggregate query models, even if they are often close.

Finally, note that our current data model does not account for data cubes, that is: we do not model the cases when some data cells are

Table 1 :

 1 Results on the first and second development set. set, and applied the combination obtaining the best MAP results on the test set (composed of the remaining 26 queries).

	10 https://en.wikipedia.org/wiki/Information_retrieval#Mean_average_precision

Table 2 :

 2 Comparing our system against baselines.

		Our system INSEE search Google search
	MAP p	0.76	0.57	0.76
	MAP h	0.70	0.46	0.69
	two baselines available prior to our work: INSEE's own dataset
	search system

https://gitlab.inria.fr/cedar/insee-crawler, https://gitlab.inria.fr/cedar/excel-extractor

http://ec.europa.eu/eurostat/statistics-explained/images/8/82/Extra_tables_Statis-tics_explained-30-11-2017.xlsx

This assumption is backed by an overwhelming majority of cases given the nature of statistic data. We did encounter some counterexamples, e.g. http://ec.europa.eu/eurostat/cache/metadata/Annexes/mips_sa_esms_an1.xls. However, these are very few and thus we do not take them into account in our approach.

https://github.com/boudinfl/kea

http://www.geonames.org/

http://www.geonames.org/export/place-hierarchy.html

http://www.lemonde.fr/les-decodeurs/

This was not actually the case; our system was developed after these articles were written.

https://research.google.com/tables

http://team.inria.fr/cedar/contentcheck

Acknowlegements This work was supported by the Agence Nationale pour la Recherche (French National Research Agency) under grant number ANR-15-CE23-0025-01.


K Moussaoui
email: kamel.moussaoui@univ-tlse3.fr

W Rubio

M Mousseigne

T Sultan

F Rezai

Effects of Selective Laser Melting additive manufacturing parameters of Inconel 718 on porosity, microstructure and mechanical properties

Keywords:

The effect of SLM parameters on porosity, microstructure and mechanical properties is studied. To this purpose, the Selective Laser Melting (SLM) technology is applied to manufacture Inconel 718 specimens. The material, the manufacturing process, the Hot Isostatic Pressure (HIP), heat treatment, observation procedures and characterisation of mechanical properties are presented. A columnar-dendritic microstructure was observed on all the SLM specimens and a Volumetric Energy Density (VED) effect on the latter was also noted. The rate of porosity varies in relation to the VED and is considerably reduced after HIP. The heat treatment erases the dendritic microstructure, significantly enhances microhardness and confers on the alloy tensile mechanical properties comparable to forged Inconel 718.

Introduction

The aeronautical, aerospace and nuclear industries have applications for which the use of conventional materials is no longer a valid option. They are then replaced by what are known as Ni-base superalloys, characterised by the conservation of their mechanical properties at high temperatures [START_REF] Zhang | Deformation characteristics of phase in the delta-processed Inconel 718 alloy[END_REF][START_REF] Anderson | Laser-assisted machining of Inconel 718 with an economic analysis[END_REF][START_REF] Song | Microstructural and mechanical properties of friction-stirwelded and post-heat-treated Inconel 718 alloy[END_REF]. Among these is Inconel 718 that can be used up to a temperature of 650 °C without any prejudicial reduction in its mechanical properties while still retaining excellent resistance to corrosion and fatigue [START_REF] Davis | Nickel, Cobalt, and Their Alloys[END_REF][START_REF] Pollock | Nickel-based superalloys for advanced turbine engines: chemistry, microstructure and properties[END_REF]. For this reason, it is chosen to manufacture parts whose operating temperatures are extremely high. However, it is difficult to manufacture workpieces from Inconel 718 using conventional machining methods due to the significant level of wear to which the cutting tools are subjected and the reduced rate of material removal [START_REF] Attia | Laser-assisted high-speed finish turning of superalloy Inconel 718 under dry conditions[END_REF][START_REF] Costes | Tool-life and wear mechanisms of CBN tools in machining of Inconel 718[END_REF].

Blanther, in 1892, was the first to file a patent relating to additive manufacturing [START_REF] Blanther | Manufacture of contour relief-maps, classification cooperative G09B29[END_REF]. However, it took until the 1980s for this process to be adopted by industrialists [START_REF] Hull | Apparatus for production of three-dimensional objects by stereolithography[END_REF]. Using this method, extremely complex workpieces can be manufactured from a CAD file and without the need to use moulds and/or cutting tools. This provides an avenue for unlimited creativity in designing parts and helps save time and reduce costs and material consumed as compared with traditional processes [START_REF] Brandl | Additive manufactured AlSi10mg samples using Selective Laser Melting (SLM): microstructure, high cycle fatigue, and fracture behavior[END_REF][START_REF] Gong | Characterization of Microstructure and Mechanical Property of Inconel 718 From Selective Laser Melting[END_REF]. Since the 1980s, additive manufacturing has developed spectacularly and some would argue that it is the manufacturing process that has been the most rapidly developed in the world [START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF][START_REF] Lu | Study on the microstructure, mechanical property and residual stress of SLM Inconel-718 alloy manufactured by differing island scanning strategy[END_REF].

Selective Laser Melting (SLM) is a powder-bed based technology in the additive manufacturing category. On manufacturing, a fine layer of metallic powder is deposited on a plate, then a high energy laser scans the layer to melt it locally in pre-defined zones. Once the first layer has been completed, the plate moves down and a second layer of metallic powder is deposited and so on until complete manufacturing of the desired part. This method allows geometrically complex workpieces with great dimensional accuracy and fine surface condition to be produced [START_REF] Vrancken | Heat treatment of Ti6al4v produced by Selective Laser Melting: microstructure and mechanical properties[END_REF].

Some studies have focused on the microstructure of Inconel 718 obtained by SLM. Amato et al. [START_REF] Amato | Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting[END_REF] observe on blank SLM specimens a development of grains and columnar microstructures that are essentially parallel to the build direction. The SLM process produces a fine columnar-dendritic microstructure that is generated by the extremely rapid cooling speeds [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF]. It also produces parts with a high level of porosity [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF], mechanical properties (mainly in fatigue) that are reduced compared with conventional processes and a high surface roughness value [START_REF] Strano | Surface roughness analysis, modelling and prediction in selective laser melting[END_REF]. This explains why SLM blanks have to be subjected to various post-treatments to reduce porosity and enhance mechanical properties. Hot Isostatic Pressing (HIP) is one post-treatment that combines a high temperature and strong pressure to reduce the porosity level. Studies have shown the beneficial effect of HIP on the porosity level (HIP at 1150 °C -100 MPa: density varying between 99.985% and 99.989%) [START_REF] Tillmann | Hot isostatic pressing of IN718 components manufactured by selective laser melting[END_REF][START_REF] Blackwell | The mechanical and microstructural characteristics of laser-deposited IN718[END_REF]. After HIP, ageing heat treatment is generally recommended for Inconel 718: 720 °C for 8 h and 620 °C for 8 h [START_REF] Davis | Nickel, Cobalt, and Their Alloys[END_REF]. This treatment ensures the germination and growth of hardening phases ′ γ and ″ γ . After ageing heat treatment, the dendritic mi- crostructure disappears, a needle-shaped δ phase precipitates at the grain boundaries, the Laves phase and carbides emerge and ′ γ and ″ γ phases disperse and precipitate further in matrix to strengthen the alloy [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF]. Parts made of Inconel 718 obtained by SLM and that are then subjected to HIP and heat treatment as described above, can significantly enhance their mechanical properties as compared with SLM blanks and compare with or even outperform forged Inconel 718 parts [START_REF] Trosch | Microstructure and mechanical properties of selective laser melted Inconel 718 compared to forging and casting[END_REF][START_REF] Amato | Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting[END_REF][START_REF] Zhang | Deformation characteristics of phase in the delta-processed Inconel 718 alloy[END_REF][START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF][START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF].

Hanzl et al. [START_REF] Hanzl | The influence of processing parameters on the mechanical properties of SLM parts[END_REF] explain that the laser velocity and power parameters have most impact on tensile mechanical properties. Their combination also affects the microstructure and the melt pool, including the surface. The various combinations of these two parameters may produce perfectly uniform surfaces or porous structures. Some studies have tested other parameters, such as the size of the laser, the thickness of the layer deposited and the distance of the scan lines for the various materials like steel 316L [START_REF] Gu | Processing conditions and microstructural features of porous 316l stainless steel components by DMLS[END_REF], Ti6Al4V [START_REF] Balla | Microstructure, mechanical and wear properties of laser surface melted Ti6al4v alloy[END_REF] and Inconel 718 [START_REF] Turker | Effect of production parameters on the properties of IN 718 superalloy by three-dimensional printing[END_REF][START_REF] Lu | Study on the microstructure, mechanical property and residual stress of SLM Inconel-718 alloy manufactured by differing island scanning strategy[END_REF][START_REF] Sufiiarov | Selective Laser Melting of the Inconel 718 nickel superalloy[END_REF]. In reality, the workpiece's final quality will depend on the combination of all these parameters. Through their experimental results, Gu et al. [START_REF] Gu | Effects of processing parameters on consolidation and microstructure of w-cu components by DMLS[END_REF] observe that the power, velocity, the thickness of the deposited layer and the distance between the scan lines have a considerable influence on densification and the microstructural characteristics during the SLM process. In order to evaluate the combined effect of these parameters, they propose a factor known as "Volumetric Energy Density (VED)" expressed in J/m 3 . Other studies use VED to take into account the combined effect of the parameters mentioned above [START_REF] Simchi | Effects of laser sintering processing parameters on the microstructure and densification of iron powder[END_REF][START_REF] Thijs | A study of the microstructural evolution during selective laser melting of ti6al4v[END_REF]. Sadowski et al. [START_REF] Sadowski | Optimizing quality of additively manufactured Inconel 718 using powder bed laser melting process[END_REF] seek to optimise the quality of the SLM process for Inconel 718 and use the factor known as "Linear Energy Density (LED)", which is the ratio between the laser power and the velocity to qualify the melt pool. They observe that when LED increases from 33 to 1500 J/m, the melt pool width increases from 100 to 520 μm and its depth increases from 13 to 300 μm. Jia et al. [START_REF] Jia | Selective laser melting additive manufacturing of Inconel 718 superalloy parts: densification, microstructure and properties[END_REF] note the same LED impact on densification and recommend a LED of 330 J/m for a densification of 98.4% when manufacturing Inconel 718. They also took an interest in the microhardness and the microstructure. As far as microhardness is concerned, they observe an increase in the latter with the increase in LED. As for the microstructure, they report that it undergoes successive changes: from coarse columnar dendrites to grouped dendrites, then fine and uniformly distributed cylindrical dendrites, with the increase in LED.

It is, however, important to note that although the basic concepts apply, the change in materials and change in the type of machine will create workpieces that are different in terms of porosity levels and mechanical properties. For this article it was decided to study the effect of the SLM parameters (laser power, velocity, distance between scan lines) through the "Volumetric Energy Density (VED)" on several criteria such as roughness, the porosity rate, the microstructure and mechanical properties. Indeed, few studies to our knowledge concern the effect of VED on the criteria mentioned above. The originality of this work lies in the influence of several VED on roughness, porosity rate, microstructure, microhardness and mechanical properties. Microstructure, microhardness and porosity rate were analysed before and after HIP+heat treatment while the mechanical properties were analysed after HIP + heat treatment.

Material and methods

The powder used in this study is a nickel alloy powder, Inconel 718.

Table 1 and Fig. 1 show the chemical composition and the metallography of the powder used. The manufacturer's grain size indicates that the size of the particles is between 5 and 25 μm. This grain size was verified using the laser method. This is a technique using the optical properties derived from the interaction between a set of particles and an incident laser beam to obtain the size distribution for the set analysed. The results are shown in Fig. 2. The particles are not very spherical and there is the presence of pores within the particles.

The powder bed laser melt additive manufacturing machine is a DMP PROX300. This machine has a YAG type laser with max. power of 450 W and a spot diameter of 70 μm. Manufacturing is performed in a protected atmosphere filled with argon (Ar). It has an automatic powder supply system and a manufacturing plate. The manufacturing process is as follows: (i) a fine layer of Inconel 718 powder is deposited by the roller; (ii) the layer of Inconel 718 powder is melted by the incident laser beam so it binds with the already solidified zones of the layer beneath; (iii) the manufacturing plate is moved down by the thickness of one layer for a new deposit of powder and new laser fusion. The laser strategy used is shown in Fig. 3. This strategy combines a different scan on each layer, with the laser scanning alternatively along the X and Y axes. This means that layer n will have the scan direction along the X-axis while layer n + 1 will be rotated by 90°and will be along the Y-axis.

In order to observe the influence of the SLM parameters on some of the previously mentioned criteria, 35 cubes with dimensions 20 * 20 * 20 mm were produced (Fig. 4). The power P was varied from 150 to 450 W, the velocity V from 1000 to 1800 mm/s and the scan Roughness appeared to be a good indicator of melt quality, which is why it was chosen as a selection criterion for the 21 remaining cubes. Surface roughness Sa was analysed on the top face (normal to Z) and the side of the cube. Only roughness results concern the 21 cubes. Indeed, the roughness criterion allowed 8 cubes (12-13-17-18-26-29-31-34) to be selected to refine observations on level of porosity, microstructure and mechanical properties. The SLM parameters of the 8 cubes are shown in Table 2. The VED was calculated using Eq. ( 1) where P is the power in W, V the scan velocity in mm/s, H the scan distance in μm and d the thickness of the layer deposited in μm. The VED will be expressed in J/ mm 3 .

= × VED P V H d . . 10 6 (1)
The surface roughness measurements were performed using an ALICONA Infinite-FocusSL optical system. The metallographic observations were performed on an Olympus optical microscope and a NOVA NanoSEM450 Scanning Electron Microscope (SEM). The specimens were polished and then etched with aqua regia (70% HCl + 30% HNO3) to observe the microstructure. The chemical composition was analysed using the Energy Dispersive Spectroscopy (EDS) method. Microhardness measurements were performed on a Buehler Micromet 5100 series system with a load of 200 g and each value was averaged out over three measurements. The heat treatment used in this study was an HIP (1160 °C, 102 MPa, 3 h and air cooling) followed by solution treatment (980 °C, 1 h and air cooling) and double ageing (720 °C, 8 h, furnace cooling + 620 °C, 8 h and air cooling). Tensile tests were performed on an Instron 8561 machine at ambient temperature. The geometry and dimensions of the tensile test specimens are shown in Fig. 5. These tensile test specimens were manufactured in two series: series A (0°) parallel to the Z-axis build and series B (90°) normal to the Z-axis build (along X). They are made from cylindrical specimens. They then underwent the heat treatment described previously and were machined. The level of porosity was established by processing of the images obtained by optical microscopy. 10 images were taken for each specimen randomly over the entire manufacturing plane (XY plane). On each image there are between 200 and 250 pores, thus meaning in total between 2000 and 2500 pores measured for each specimen to determine the level of porosity. The drawback with this method was the considerable effort that had to be devoted to preparation of the specimens.

Results and discussion

Roughness

The results show a roughness Sa going from 6.7 to 35 μm on the cube's top face and from 8.5 to 42 μm on the cube's side. These values are very close and indicate good uniformity of roughness over the entire cube. A curve is plotted on the graph of Fig. 6 to show some roughness values (cube top face Sa) to observe the effect of the scan velocity V and power P. It can be seen that the increase in velocity and power leads to greater roughness while lower velocities and powers generate less roughness. No significant hatching effect H was observed and use of VED was not decisive for roughness. However, it is important to note that the quality of the final surface will depend mainly on the power/ velocity relation.

The following results concern the 8 cubes (12-13-17-18-26 -29-31-34) chosen after the roughness study. These 8 cubes have a roughness Sa of between 6.7 and 15.46 μm for the top face of the cube and between 8.5 and 17.6 μm for the side of the cube.

Microstructures and porosity

As-deposited by SLM

The physics involved during the laser beam melting process of a powder bed is illustrated schematically in Fig. 7. This Figure shows a cross-section of a powder bed on the scale of particles of powder lying on a dense substrate. In the zone where the laser beam reaches the powder bed, the particles of powder are heated extremely rapidly, and the local temperature increases to form a melt pool that will then solidify. Several physical phenomena will intervene and combine to form the final material and its accompanying microstructure.

Fig. 8 shows a 3D cube that is built from the observations on specimen 12 on an optical microscope. The line by line SLM and then layer by layer SLM manufacturing characteristics are clearly visible. On the XY plane the scanning strategy used in the present study can be observed. The XZ and ZY planes illustrate the morphology of the melt pool. This morphology is in the form of a parabolic arc that indicates a Gaussian energy distribution of the laser. Similar morphologies have been observed for SLM manufacturing of Inconel 718 by other researchers [START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF][START_REF] Zhang | Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy[END_REF]. This morphology was observed on all the specimens in this study.

Fig. 9 shows a columnar dendritic microstructure that is mainly parallel to the Z-axis build (shown by the white arrow). This microstructure is characteristic of the microstructures obtained by SLM for Inconel 718. It also indicates a very rapid cooling speed of around 10 5 °C/s [START_REF] Vilaro | Microstructural and mechanical approaches of the selective laser melting process applied to a nickel-base superalloy[END_REF]. Columnar grains with a cellular structure and columnar grains with very fine dendrites can also be distinguished in this microstructure. The melt pool boundary shows a solidification front from which a different structure can grow (switch to a cellular structure) leading either to a change in orientation of the dendrites or a continuity of the dendrites through the solidification front. The high temperature gradients generate an epitaxial solidification phenomenon [START_REF] Amato | Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting[END_REF] that can produce grain growth through several melt pool. All these types of structure can also be observed in a single melt pool (Fig. 9(a)). It can be noted that the melt energy affects more than one layer and will thus melt layers that have already solidified several times. This is a phenomenon that is sought for to bind the layers to each other and make the material more uniform. The increase in VED will lead to a microstructure with longer and very tightly bound dendrites (Fig. 9(b)). Jia et al. [START_REF] Jia | Selective laser melting additive manufacturing of Inconel 718 superalloy parts: densification, microstructure and properties[END_REF] note the same effect on the microstructure of Inconel 718 obtained by SLM. Another observation on the effect of the increase in VED on the microstructure relates to the columnar dendrites that seem to be more oriented along the build-axis. The increase of the VED will produce a larger and warmer melt pool. This results in a high thermal gradient and a high cooling rate. This phenomenon will produce fine columnar dendrites. Zhang et al. [START_REF] Zhang | Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy[END_REF] measured a dendrite spacing of about 0.6 μm. They tell us that this spacing is small compared to the Inconel obtained by conventional method because of the very high cooling rates in SLM. Mostafa et al. [START_REF] Mostafa | Structure, texture and phases in 3d printed IN718 alloy subjected to homogenization and HIP treatments[END_REF], measured a dendrite spacing ranging from 0.6 to 1.25 μm in SLM. All these observations are similar for the ZY plane, while for the XY plane a mainly cellular structure with less dendrites can be seen. Fig. 10 shows several types of defects: pores by lack of fusion and/or material and spherical pores. What can mainly be seen are spherical pores that were formed during the melt process either by the trapping of protection gases (here Ar) or by the gases generated by melting (sufficiently rapid cooling that traps the metallic vapour). All these types of pores were observed on the three planes. Tillmann et al. [START_REF] Tillmann | Hot isostatic pressing of IN718 components manufactured by selective laser melting[END_REF] showed the presence of argon in the spherical pores with a slightly greater mean Ar content of 0.3 ppm in Inconel 718 specimens obtained by SLM. They suggest that even if the measured value seems to be very low, the Ar trapped in the structure may have a major influence on the mechanical properties and post-treatment. In high temperature conditions, as during HIP, machining or in various applications, the trapped Ar dilates (gas laws) and causes stresses that can lead to elastic or plastic deformations. They also indicate that only the pores without gas could be perfectly closed by an HIP. The spherical type defects are located more to the interior of the melt pools, while lack of melting and/ or matter type defects are to be found more on the boundaries of the melt pools and the overlapping of the layers (Fig. 10(b)).

Fig. 11 shows the micrography of the XY plane of specimen 29 obtained with a VED = 61.2 J/mm 3 . A significant reduction in pores can be seen and above all of those of the lack of material or melt type as compared with specimen 31 (Fig. 10(a)). This reduction was observed for the three planes of specimen 12 and showed a good similitude in the level of porosity between the three planes. Fig. 11(b) meanwhile reports the level of porosity in relation to VED. This level of porosity varies from 0.48% to 1.35%. As can be seen, VED has a significant impact on the level of porosity. Indeed, when VED increases, this leads to a reduction in the level of porosity. This observation seems coherent since Fig. 7. Schematic overview of the physicals phenomenons that happen in the interaction zone between laser radiation and powder bed. greater energy is used to melt the powder, which has the effect of improving melting and a reduction in defects. Other authors have noted this phenomenon [START_REF] Jia | Selective laser melting additive manufacturing of Inconel 718 superalloy parts: densification, microstructure and properties[END_REF].

SLM plus HIP and heat treatment

The specimens were subjected to an HIP and a heat treatment (solution and ageing). The conditions were described above. HIP is mainly used to reduce porosity. However, Tillmann et al. [START_REF] Tillmann | Hot isostatic pressing of IN718 components manufactured by selective laser melting[END_REF] observe that HIP also modifies the microstructure of SLM Inconel 718: the microstructure no longer resembles the typical microstructure obtained by SLM, the grains are bigger, and they no longer have an orientation along the build axis. Solution treatment causes the transformation of one or more constituents into a solid solution and, by rapid cooling, these constituents are kept in that solution. Ageing treatment (conducted in two stages) causes hardening by precipitation. This treatment ensures germination and growth of the hardening phases ′ γ (Ni3(Ti, Al)) and ″ γ (Ni3Nb) in the matrix γ up to a suitable volume fraction of around 15-20% for ″ γ [START_REF] Jambor | Phase transformations in nickel base superalloy INCONEL 718 during cyclic loading at high temperature[END_REF], that confers its excellent mechanical properties on the alloy. Precipitation of the ′ γ and ″ γ phases mainly arises during the first stage at 720 °C, while the function of the second stage at 620 °C is mainly to ensure uniformity of the microstructure [START_REF] Max | Comportement mecanique et couplage mecanique-oxydation dans l′alliage 718: effet des elements en solution solide[END_REF]. For the Inconel 718 alloy, solution heat treatment and double ageing is needed [START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF].

Figs. 12 and 13 show the microstructure after HIP and a heat treatment. The dendritic microstructure has completely disappeared. The grain size is very heterogeneous and equiaxial and mainly columnar grains oriented in the build direction can be seen. The grain boundaries are mainly constituted of δ and MC carbides. All these ob- servations concern the full set of specimens and the three planes. In the study by Chlebus et al. [START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF], they mention that heat treatment does not completely eliminate the texture, as it does not entirely change the columnar shape and crystallographic orientation of the solid solution grains.

The δ phase (Fig. 12, arrow 3) germinates mainly at the grain boundaries and its chemical composition is identical to that of the ″ γ phase (Ni3Nb). It has an acicular and pebbly morphology. The growth of the δ phase can locally reduce the volume fraction of the ″ γ phase ( ″ γ becomes a source of Nb for δ) and thus impairs local mechanical properties. However, when it is in a small quantity precipitated on the grain boundaries discontinuously, this phase can improve creep behaviour properties [START_REF] Ter-Ovanessian | Etude comparative de differents superalliages base Ni pour ressorts de systemes de maintien[END_REF]. The MC carbides (Fig. 12, arrows 1 and 2) are predominantly block-shaped and are non-uniform distributed within the grain as well as at the grain boundaries. MC intragranular carbide can interfere with the movement of dislocations but gives low matrix strength to the strength produced by ″ γ precipitation. This carbide, if it is on the surface of the part, can be a site of crack initiation or oxidation under thermal stresses, producing a notch effect unfavorable to fatigue [START_REF] Donachie | Superalloys: A Technical Guide[END_REF]. The MC carbide at the grain boundaries promotes the transition from transgranular to intergranular fracture mode. When the carbides are closely distributed along the grain boundaries, the microcracks easily join together and facilitate the intergranular fracture. The MC carbides at grain boundaries, distributed in small quantities and of appropriate size, can limit the movement of grain boundaries, slow grain growth, and may increase creep and fatigue strength [START_REF] Sundararaman | Carbide precipitation in nickel base superalloys and their effect on mechanical properties[END_REF][START_REF] Sims | Superalloys II: High-temperature Materials for Aerospace and Industrial Power[END_REF]. The ′ γ and ″ γ phases cannot be observed under the SEM as their size is generally less than 20 nm [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF].

On Fig. 13, a comparison is made between two specimens, one with a low VED and the other a high VED. It can be seen that the porosity has diminished very significantly. The level of porosity measured on the XY plane is less than 0.01% for all the specimens. The HIP has considerably reduced the size and level of porosity. The microstructure obtained after heat treatment is largely similar between the specimen with a low VED and a high VED. This shows that heat treatment largely erases the SLM microstructure obtained with different levels of VED and generates a new microstructure similar to that of all the specimens.

Mechanical properties

Microhardness

Among mechanical properties, microhardness is a major concern for parts manufactured by SLM. Fig. 14 shows the microhardness results in relation to VED. Here, the results for as-deposited by SLM vary between 310 and 334 HV. No VED effect can be seen on these results. These levels of microhardness are corroborated by other studies [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF][START_REF] Zhang | Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy[END_REF][START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF]. It should be noted that the main source of hardening of Inconel 718 is the precipitation of the ′ γ and ″ γ phases [40]. Another element that can increase hardening is porosity. In our study the porosity rate varies between 0.48% and 1.35%. This variation remains relatively small to have an effect on microhardness. In view of the above analysis, the VED variation range (31-61 J/mm 3 ) studied here did not sufficiently precipitate these phases to observe a visible effect on the microhardness of the specimens before HIP + heat treatment. On this point, Jia et al. [START_REF] Jia | Selective laser melting additive manufacturing of Inconel 718 superalloy parts: densification, microstructure and properties[END_REF] observe an increase of microhardness (331.9-395.8 HV) for a range of variation of energy density ranging from 180 to 330 J/m. According to them, this improvement of the microhardness produced by the increase of energy density is the consequence of the decrease porosity rate, grains refinement and strengthening of precipitations and solid-solutions. According to our analysis of the results of Jia et al. the improvement in microhardness is due more to the porosity's decrease (from 26.4% to 1.6%) caused by the increase in energy density. A heat treatment is necessary to further enhance microhardness despite the way the material is obtained (by heating and very rapid cooling) that is generally beneficial for that quality. The results for HIP+HTed range between 461 and 492 HV. This remarkable improvement is mainly due to solution heat treatment and ageing that causes the precipitation of the ′ γ and ″ γ phases in the matrix γ. These values correlate well with other studies using the same heat treatment or even better [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF][START_REF] Zhang | Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy[END_REF][START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF]. They are also higher than those obtained for a forged material having undergone heat treatment (430-460 HV [START_REF] Davis | Nickel, Cobalt, and Their Alloys[END_REF]).

Tensile properties

Fig. 15 shows the results of tensile tests (σ t , σ 0.2 , ϵ f ) for series A (0°: parallel to the Z-axis build) and series B (90°: perpendicular to the Zaxis build). With series A, the values vary for tensile stress (σ t ) between 1334 and 1375 MPa, for the elastic limit (σ 0.2 ) between 1084 and 1124 MPa and for elongation at fracture (ϵ f ) between 17.5% and 20%. With series B, the values vary for σ t between 1376 and 1392 MPa, for σ 0.2 between 1110 and 1136 MPa and for ϵ f between 18% and 25%.

No significant visible effect of VED is seen on the tensile mechanical properties. However, a difference is noted between series A and series B for all tensile properties (σ t , σ 0.2 , ϵ f ). Tensile mechanical properties are distinctly better when the specimen is perpendicular to the Z-axis build (series B). According to Amato et al. [START_REF] Amato | Microstructures and mechanical behavior of Inconel 718 fabricated by selective laser melting[END_REF], this difference between specimens parallel to and perpendicular to the build axis derives from the direction of the columnar grains. There are much more grain boundaries is perpendicular to the build axis for specimens at 90°than parallel to the build axis for specimens at 0°. Other studies have observed the same difference [START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF][START_REF] Ni | Anisotropic tensile behavior of in situ precipitation strengthened Inconel 718 fabricated by additive manufacturing[END_REF]. Heat treatment played a perfect role in enhancing mainly the mechanical characteristics by precipitation of the ′ γ and ″ γ phases. The values for tensile mechanical properties are equivalent or even better as compared with those for other studies on Inconel 718 obtained by SLM and having used the same heat treatment [START_REF] Wang | The microstructure and mechanical properties of deposited-IN718 by selective laser melting[END_REF][START_REF] Zhang | Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy[END_REF][START_REF] Chlebus | Effect of heat treatment on the microstructure and mechanical properties of Inconel 718 processed by selective laser melting[END_REF]. As compared with forged and aged Inconel 718 (σ t = 1100 MPa, σ 0.2 = 830 MPa, ϵ f = 31%), these values are higher for σ t and σ 0.2 except for ϵ f . As for forged and aged Inconel 718 (σ t = 1600 MPa, σ 0.2 = 1400 MPa, ϵ f = 16%), σ t and σ 0.2 are lower except for ϵ f [42].

Conclusions

The present study focused on the effects of SLM parameters through Volumetric Energy Density (VED) on porosity, microstructure and mechanical properties. The main conclusions can be summarised as follows:

• Roughness varies between 6.7 and 35 μm on the top face of the cube and between 8.5 and 42 μm on its side. The low velocities and powers generate reduced roughness while an increase in velocity and power leads to greater roughness. It is important to note that the quality of the final surface will depend mainly on the power/velocity relation.

• The SLM microstructure is a columnar dendritic microstructure or- iented parallel to the build axis. This microstructure may enlarge through several layers and is made up of columnar grains with a cellular structure and columnar grains with very fine dendrites. The increase in VED leads to a microstructure with longer and tighter dendrites that are more oriented along the build axis.

• Several types of defects were observed: pores by lack of melting and/or of material and spherical pores. Mainly spherical pores were seen, located in the melt pools. Defects of the lack of melt and/or material type were located at the melt pool boundaries and the overlapping of layers. The level of porosity varied between 0.48% and 1.35%. The increase in VED leads to a reduction in the level of porosity.

• After HIP and heat treatment, the dendritic microstructure has completely disappeared and conceded to a microstructure with equiaxial grains and mainly columnar grains oriented in the build direction. The grain boundaries were mainly composed of δ and MC carbides. The VED effect on the microstructure was no longer visible and it would appear that heat treatment removes a fair share of the SLM microstructure obtained with various levels of VED. The level of porosity was significantly reduced for all the specimens (less than 0.01%) thanks to HIP.

• SLM microhardness varies between 310 and 334 HV. No VED effect was observed on these results. After heat treatment, microhardness increases remarkably and varies between 461 and 492 HV. Indeed, solution heat treatment and ageing leads to hardening by precipitation of the ′ γ and ″ γ phases in the matrix γ.

• No significant visible effect of VED on tensile mechanical properties was observed. However, a difference was noted between parallel (0°) and perpendicular (90°) specimens in relation to the build axis. Heat treatment improved the tensile mechanical properties but removed the VED effect. These tensile results are better than those obtained for forging-annealing and slightly poorer than those for forging-ageing.

Fig. 1 .

 1 Fig. 1. SEM metallographic image of powder etched cross-section showing the internal microdendritic microstructure and pores in particles.

Fig. 2 .

 2 Fig. 2. Particle size distribution of Inconel 718.

Fig. 3 .

 3 Fig. 3. Laser scanning strategy used in SLM experiments.

Fig. 4 .

 4 Fig. 4. Inconel 718 specimen model.

Fig. 5 .

 5 Fig. 5. Geometry and dimensions of the tensile specimens. Fig. 6. Effect of power (P) and scanning velocity (V, with V0 < V1 < V2) on roughness Sa of the cube face.

Fig. 8 .

 8 Fig. 8. Optical metallographic image of Inconel 718 in as-built condition in three mutually perpendicular planes of the polished section for specimen 12. The laser scanning tracks are visible in the 3 planes. The build direction is indicated by Z axis.

Fig. 9 .

 9 Fig. 9. SEM micrographs of XZ plane showing columnar cellular (G) and fine dendrites (shown by arrow). Z is build direction.

Fig. 10 .

 10 Fig. 10. SEM micrographs showing the different types of defects of SLMed Inconel 718. VED = 31.75 J/mm 3 . The circle indicates defects of the spherical type and the hexagon indicates the lack of fusion and/or material.

Fig. 11 .

 11 Fig. 11. (a) SEM micrographs of specimen 29 with VED = 61.2 J/mm 3 . (b) XY plane porosity rate versus VED for all specimens.

Fig. 12 .

 12 Fig. 12. SEM micrographs of specimen 12. (a) plane XY. (b) plane ZY. MC carbides on grain boundaries (arrow 1) and on the layer interface (arrow 2) accompanied by δ-phase precipitates (arrows 3).

Fig. 13 .

 13 Fig. 13. SEM micrographs of specimen 17 and 13. Z is build direction.

Fig. 14 .

 14 Fig. 14. Microhardness of SLM Inconel 718 specimens as-built and HIP + HTed.

Fig. 15 .

 15 Fig. 15. Mechanical properties of Inconel 718 after HIP plus HTed. σ t is tensile strength, σ 0.2 is yield strength and ϵ f is elongation at fracture.

Table 1

 1 Chemical composition of Inconel 718 powder.

	Element	Ni	Cr	Fe	Nb	Mo	Ti	Al
	wt%	54.19	20.58	15.14	5.13	3.04	0.95	0.67

Table 2

 2 Parameters of SLM for the 8 cubes.

	Specimen	VED
	number	(J/mm 3 )
	12	40.8
	13	51
	17	31.75
	18	39.7
	26	40.8
	29	61.2
	31	31.75
	34	47.6

Acknowledgements

The research leading to these results has received funding from the French Single Inter-Ministry Fund, under ALMINCO Project agreement. The authors would like to thank the following institutions and companies for their contributions and support: Rgion Midi-Pyrnes and PRISMADD.