Sara Houhou
email: sara.houhou@lip6.fr

Souheib Baarir
email: souheib.baarir@lip6.fr

Pascal Poizat
email: pascal.poizat@lip6.fr

Philippe Quéinnec
email: philippe.queinnec@irit.fr

A Direct Formal Semantics for BPMN Time-Related Constructs

Keywords: BPMN, Timed Models, Workflows, Collaborations, Formal Verification, Alloy, Tool

BPMN supports the design of intra-organization workflows and inter-organization collaborations. This rich notation includes elements to deal with models where time is central. However, the expressiveness of the BPMN time-related constructs hampers the definition of a formal semantics including them, and the provision of formal analysis means for timed process models. We propose here a first-order logic semantics for a subset of BPMN that includes its time-related constructs. With reference to related work, we support the specification of datetimes, durations, and cycles, using ISO-8601 formats as specified in the standard. Our approach is tool-supported by a model transformation into the Alloy formal language and its bounded counter-example generator. Our tool and model database are open source and freely available.

INTRODUCTION

A Business Process (BP) is a set of activities that are organized in order to reach some objective. Business Process Modeling Notation(BPMN) enables one to model both single processes using workflows but also collaborations where communication coordinates processes in different organizations. In both cases, time can play a part in the way the process(es) execute, e.g., with deadlines before which one has to agree on a commercial offer or with sub-processes being regularly started after some duration.

To support this, BPMN defines a set of timerelated events: timer start events (T SE) -to start some process, timer intermediary catch events (T ICE)to wait for some condition to be fulfilled, and timer boundary events (T BE), interrupting or not, to stop an activity or run a parallel one. All three kinds of events depend on a time-related condition defined in their TimerEventDefinition (OMG, 2013).

There are also three kinds of TimerEventDefinitions: timeDate (at some date-time, e.g., at 5:30 pm on March, 24th, 2020), timeDuration (after some amount of time, e.g., after 1 hour and 30 minutes), and timeCycle (repeated several times, with a duration between each instance and possibly after/before a given date-time, e.g., after 1 hour and 30 minutes, 3 times, starting from 5:30 pm on March, 24th, 2020). To give the associated piece of information, BPMN relies on the ISO-8601 standard (ISO8601, 2004). Table 1 gives a synthetic view of time-related events in BPMN w.r.t. the ISO-8601 standard. No explicit formal semantics for BPMN time-related features is given in the standard. Further, the ISO-8601 description of time information is quite complex. This makes it more difficult to perform formal analysis of process models before, e.g., running them on process engines.

In addition, a lot of effort has been done to identify the most common time-related scenarios from a business perspective, leading to Process Time Patterns [START_REF] Lanz | Workflow time patterns for process-aware information systems[END_REF][START_REF] Lanz | Time patterns for process-aware information systems[END_REF][START_REF] Lanz | Process time patterns: A formal foundation[END_REF]. Formally assessing the suitability of BPMN to support these patterns is desirable. However, this requires first to define a formal operational semantics for time-related features in BPMN. This issue has been addressed in several proposals (see Section 5). Still, these proposals often leave apart several features related to time-related events in the broader sense (Tab. 1). Contribution. In a previous work [START_REF] Houhou | A first-order logic semantics for communicationparametric BPMN collaborations[END_REF], we have defined a formal semantics for a sub- set of BPMN (Fig. 1, but for time-related events), with a focus on BPMN communication constructs and different communication models. We also had defined a tool, fbpmn, to support the formal analysis of processes, and generate and animate counter examples.

In the paper at hand, we extend this work by supporting the expressive time-related features of BPMN, including the use of the ISO-8601 standard, and show how we can support the Process Time Patterns. The proposed semantics is directly defined in terms of First-Order Logic (FOL), rather than through a mapping to some formal language. This choice makes it possible for researchers to map the FOL semantics to verification frameworks of their choice like (Alloy with SAT solvers) as we did here; TLA+ with the TLC model-checker (as we did before), SMT, or others). To support the formal verification of processes, we translate the proposed semantics in Alloy.

Case study. Fig. 2 presents a BPMN diagram of a simplified reviewing procedure for a scientific paper in a special issue of a journal. The scenario involves three participants that act in a collaboration diagram which are PC chair, Author, Reviewer. For simplification, we consider only one author and only one reviewer. This model is elaborated based on the following scope statements:

• The author sends a paper to the Journal PC Chair through the submit paper send task. Then, he/she will wait until the arrival of the notification response. If he/she doesn't receive a notification by "2021-09-18 T 00:00" the author withdraws his/her paper.

• The PC Chair starts when the specified date and time, "2021-01-17 T 00:00", of the CFP is reached. This is reflected by the timer start event of the process at the Journal PC Chair. Then, it waits for submissions. The receive activity is authorized until the specified close date, given as "2021-03-17 T 00:00". When the process receives a research paper, he/she assigns it to a reviewer via the send task "assign paper". To avoid delay for the response review process, he/she sends before the deadline date a reminder two times in a period of 15 days between. This is reflected by a non interrupting boundary time event associated with the receive review task, "R2/ P15D / 2020-04-29 T 00:00:00".

• The Reviewer process receives a Review Request message to starts. The reviewer starts preparing a review, and he/she sends it back to the PC Chair when it is ready.

• After the PC Chair has received a review, he/she prepares the acceptance/rejection letter, or a borderline letter if the paper requires further improvements. Then, he/she attaches the review to the notification letter and sends it to the author at the notification date and time specified in the CFP ("2021-05-16 T 00:00"). Even if the PC Chair has reached a decision before that date, he/she waits for this date before sending the notification. This is reflected by an intermediate timer event.

Overview. The remainder of this paper is structured as follows. Section 2 gives an informal overview of the BPMN execution semantics, including timerelated features. Section 3 then details our proposed formalization for them. The implementation of our semantics in Alloy, verification, and evaluation are discussed in Section 4. We end up with a comparison to related work in Section 5 and a conclusions in Section 6.

OVERVIEW OF THE BPMN EXECUTION SEMANTICS

In this section we informally survey the semantics of the BPMN elements that we support (Fig. 1). To maintain traceability with the standard, we use a token-based approach, with tokens on both nodes and edges. We define an execution model based on two predicates, Start (St) and Complete (Ct). Their definition depends on the BPMN element taken in consideration. In the next section we give the formal definition for time-related features, together with activities (tasks and sub-processes) and the event-based gateway, since time has an impact on their semantics. The semantics for the other BPMN constructs is kept from [START_REF] Houhou | A first-order logic semantics for communicationparametric BPMN collaborations[END_REF].

Starting and terminating. Three kinds of events are used for the starting of a process 1 : none (NSE), message (MSE), and timer (T SE) start events. All three are defined only through completion predicates.

They complete by initiating the process to which they belong and by generating a token on their outgoing edges. MSE and T SE are only ready to complete if (i) they are active and, respectively, (ii) a specified message has arrived on one of their incoming message flow edges, or the (global) clock has reached a given deadline. Two kinds of events are used for the termination of a (sub-)process: none (NEE) and terminate (T EE) end events. They start by moving a token from one of their incoming edges to themselves.

A T EE has an additional behavior. It drops down all the remaining tokens of the process or sub-processes to which it belongs.

Activities. They are the main working units in a process. We make the distinction between a composite activity, or Sub-Process (SP), and an atomic activity, or Task (T ). The latter can be an abstract (AT ), send (ST ), or receive (RT ) task. All activities have the same basic behavior. They start by moving a token from an incoming edge to themselves. When the activity is associated to a timer event, it does some additional work that we will specify in the next paragraphs.

Gateways. They are used to manage the control flow 1 NSE can also be used to start a sub-process.

of a process. A gateway can be Parallel (AND) to model the simultaneous execution of all control flows in a set, Inclusive (OR) to model the simultaneous execution of a subset of control flows in a set, Exclusive (XOR) to model the choice of one control flow in a set, or Event-Based (EB) to model the choice of one control flow in a set, based on external event triggers (message or time conditions). An EB gateway is a kind of deferred choice since its completion depends on external events. It completes by moving the token it owns on the triggered event outgoing edge. In this paper we focus on EB gateways due to the importance of priority aspects in their formal execution semantics in presence of time-related features.

Intermediate events. They are events that can occur during the process execution. In our work, we consider the Message and Timer intermediate events.

For the Message ones, we support message catching (CMIE), message throwing (T MIE), and boundary (interrupting or not) message (MBE) events. For the Timer ones, that constitute the focus of this work, we support the following:

• Timer Intermediate Catch Events (T ICE) that act as a delay mechanism configured either by a duration (T ICE p2 ) or a fixed date (T ICE d ). Such an event waits for the specified duration or date before letting the control flow on which it is located continue.

• Timer Boundary Events (T BE) that are attached to an activity. Such an event can be either interrupting (T BE ), i.e., it interrupts the running of the activity it is attached to, or non- interrupting (T BE ⊕ ). The start of an activity with timer boundary events causes the activation of local clocks for the boundary events attached to it.

-A T BE acts as a deadline for an activity. If the activation token remains on the activity more than a specific duration, or fixed date, the timer event interrupts the activity it is attached to. We separate T BE d and T BE p : A T BE d is a T BE configured with a date, while a T BE p is configured with a duration.

-A T BE ⊕ can be configured with a date (T BE ⊕ d ), a duration (T BE ⊕ p ), or a time cycle (T BE ⊕ c ). T BE ⊕ d and T BE ⊕ p define the same behavior as T BE d and T BE p (respectively), without cancelling the activity they are attached to. T BE ⊕ c might be triggered multiple times while the activity it is attached to is active. The number of cycles can either be fixed or unbounded. The time cycle definition associated to a timer event may have different configurations: (i) T BE ⊕ c(start) defines a number of recurrences for the timer event triggers separated by a period and where the first trigger is done relatively to a fixed start date; (ii) T BE ⊕ c(end) defines a number of recurrences for the timer event triggers separated by a period and where the last trigger is done before the fixed end date; (iii) T BE ⊕ c(p) defines a number of recurrences for the timer event triggers separated by a period.

BPMN TIME FORMALISATION

In this section we extend the formal semantics that we proposed in [START_REF] Houhou | A first-order logic semantics for communicationparametric BPMN collaborations[END_REF], to handle time constructs with associated ISO-8601 time information. We rely on a (typed) graph representation of the workflow and collaboration models where types correspond to kinds of BPMN elements as given in Fig. 1 and Section 2, e.g., T BE for Timer Boundary Events and T BE p for interrupting Timer Boundary Events with a duration information. Roughly speaking, We consider two sets of basic elements types: Nodes, noted by T Nodes and Edges, noted by T Edges as follows:

• T Nodes = {NSE, MSE, T SE,CMIE, T MIE, MBE, T SE, NEE, T EE, MEE, XOR, OR, EB, AND, AT, ST, RT, SP} ∪ T ICE ∪ T BE, where:

-T ICE = {T ICE p , T ICE d } -T BE = T BE ∪ T BE ⊕ , with * T BE = {T BE d , T BE p } * T BE ⊕ = {T BE ⊕ d , T BE ⊕ p } ∪ T BE ⊕ c , with T BE ⊕ c = {T BE ⊕ c(start) , T BE ⊕ c(start) , T BE ⊕ c(p) } • T Edges = {NSF,CSF, DSF, MF}

Syntax

A BPMN model is seen as a typed graph (Def. 1), where types corresponding to the BPMN elements are associated to nodes and edges. The BPMN standard defines three time categories: timeDate, that specifies a fixed date and time, timeCycle, that specifies repeating intervals, and timeDuration, that specifies the amount of time a timer should run before firing. Formally, we define three time categories, Ctime = {T date , T duration , T cycle }, and the following time structures to characterize the time constraints, timeVal = Date ∪ Duration ∪Cycle: • cat E : E → T Edges gives the type of an edge. In the following, we write N T (resp. E T ) to denote the subset of nodes (resp. edges) of type T, e.g.,

• Date ⊆ N represents
N T = {n ∈ N | cat N (n) ∈ T }.
By abuse of notation, in the following we write N t instead of N {t} , e.g., N NSE instead of N {NSE} , and similarly for E t . • src/tgt : E → N give the source/target of an edge,

• R : N {P,SP} → 2 N∪E gives the set of nodes and edges that are directly contained in a container (process or sub-process).

• msg t : E MF → M gives the message associated to a message flow,

• attachedTo : N BE → N A , gives the activity to which a boundary event node is attached,

• isInterrupt : N BE → Bool, denotes whether a boundary event node is interrupting or not,

• f time : N Timer → Ctime × timeVal, associates a time category and a value to the timer nodes.

Several tools supports modelling with BPMN 2.0, e.g. Camunda, Eclipse modelling, Signavio. . . , and with various levels of completeness. These tools authorize modelling uncompleted models e.g., gateways without incoming and outgoing edges. To be analyzed, the BPMN models must be structurally wellformed. These well-formedness rules have been omitted due to lack of space. Notation. R + is the transitive closure of R. To denote the projection of the function f time on a component of its co-domain, we use the notation Ctime (resp.

) : N → 2 E is used to com- bine in (resp. out) with E T , in T (n) = in(n) ∩ E T and out T (n) = out(n) ∩ E T . procOf : N → N P returns the container process of a given node, procOf (n) = p if and only if n ∈ R + (p).

Semantics

To describe a process execution, while maintaining traceability with the standard (OMG, 2013), we rely on a token-based semantics. We define an execution model using two predicates (St, Ct) for each node type. These correspond to, respectively, the enabling of a node to start its execution, and the enabling of a node to complete its execution. Some nodes only have a start transition (e.g., end events), and others only have a completion transition (e.g., gateways). The formal definition of these predicates relies on the notion of state of the BPMN Graph.

State Notion

It represents the global configuration of a BPMN model (workflow or collaboration), at any moment of its execution.

State. A state of a BPMN graph G= (N, E, M, cat N , cat E , src,tgt, R, msg t , attachedTo, isInterrupt, f time) is a tuple s = (m n , m e , l c , g c , rec) such that:

• m n : N → N and m e : E → N, are marking functions, that associate a number of tokens to nodes and edges (respectively).

• l c : N Timer → N, is a local clock for the time spent on a timer node.

• g c ∈ N, is a global clock for the current time on the whole model.

• rec : N T BE ⊕ c → N ∪ {ι} represents, for each activated non-interrupting timer boundary event node with a finite cycle, the number of occurrences that remains to be executed.

The set of all states of a BPMN graph is denoted by States.

Initial

state. The initial state s o = (m n 0 , m e 0 , l c 0 , g c 0 , rec) of a BPMN graph is defined as follows:

• Nodes own 0 token, except for the initial nodes of a process that start with 1 token:

∀n ∈ N, m n 0 (n) = 1 if ∃p ∈ N P , n ∈ N SE ∩ R(p), 0 otherwise
• Edges own 0 token: ∀e ∈ E, m e0 (e) = 0;

• The global clock is initialized to a specific date and time (w.r.t. a referential 3 ): g c 0 ∈ N;

• Local clocks are initialized to zero: ∀n ∈ N Timer , l c 0 (n)=0;

• Redundancy variables are initialized with the recurrence number (if it exists):

∀n ∈ N T BE ⊕ c , ∃ m, d, p ∈ N, f time(n) timeVal = (m, p) ∨ f time(n) timeVal = (m, d, p) ⇒ rec 0 (n) = m
To formalize the semantics, we introduce the following predicates:

3 referential: an absolute date and time

• mayComplete(n) : N SP → Bool, returns true if the sub-process may complete, i.e., if there is a token on one of its end events, and there is no token on the rest of its elements (except for end events). This predicate is defined only for the sub-process where interruption nodes may attached to it.

∀n ∈ N SP , mayComplete(n) de f ≡ (m n (n) ≥ 1) ∧ ∀e ∈ (R(n) ∩ E), (m e (e) = 0) ∧ ∃nn ∈ R(n) ∩ N EE , (m n (nn) ≥ 1) ∧ ∀x ∈ R(n) ∩ (N \ N EE ), (m n (x) = 0)
• run is a predicate that increases the local clock of each active timer events node and the global clock at once.

run()

de f ≡ ∀n ∈ S, (l c (n) = l c (n)+1)∧ (g c = g c +1)
• is a predicate that denotes marking equality but for nodes and edges given as parameter, (X) means "nothing changes except for X":

(X) de f ≡ ∀n ∈ N \ X, m n (n) = m n (n) ∧∀e ∈ E \ X, m e (e) = m e (e)
• t is a predicate that denotes that clocks do not change except for the local ones for the nodes in X:

t (X)

de f ≡ g c = g c ∧ ∀n ∈ N Timer \ X, l c (n) = l c (n)
The formal semantics of the BPMN time-related constructs is given in Table 3. Here, we consider that m n and m n (resp. m e and m e ) denote two successive markings of a node (resp. edge) in the execution semantics. The semantics of the elements in Fig. 1 and not in Table 3 is kept from [START_REF] Houhou | A first-order logic semantics for communicationparametric BPMN collaborations[END_REF].

Let us consider a subset of timer nodes, called S, that groups the nodes that satisfy one of the following conditions: (i) all starting timer nodes that have a token and the global time date of the system does not reach their fixed time date (ii) all intermediate timer nodes that have an inactive local clock and have a marked incoming edge, or if they follow an event based gateway and the latter has a marked incoming edge, (iii) all boundary timer nodes attached to an active activity and their local clock is not active, or (vi) all active timer nodes (i.e., their local clocks are greater than 0 and they didn't reach their timing limits) as follows:

S de f ≡ {n ∈ N T SE | (Timing(n) < g c ) ∧ (m n (n) = 1)} ∪ {n ∈ N T ICE | ∃e ∈ in SF (n), (l c (n) = 0) ∧ (m e (e) > 0)} ∪ {n ∈ N T ICE | ∃e ∈ in SF (src(in SF (n))), (l c (n) = 0) ∧ (m e (e) > 0)} ∪ {n ∈ N T BE | (l c (n) = 0) ∧ (m n (attachedTo(n)) > 0)} ∪ {n ∈ N Timer | timing(n) > l c (n) > 0}
Let Y be the subset of timer nodes in the BPMN graph that are ready to fire:

Y de f ≡ {y ∈ N Timer | l c (y) ≥ Timing(y)}
To facilitate the reading of the transition relation, we define the following predicates:

• step defines a step of execution for a given node:

step(n) de f ≡ St(n) ∨Ct(n)
• f ztime denotes time equality for the local clock of all timer nodes given as parameter:

f ztime(Z) de f ≡ ∀z ∈ Z, l c (z) = l c (z)
The transition relation distinguishes two cases. If at least a timer is ready to fire (Y = / 0), then a timer fires (it does a step) or an event-based gateway that precedes a firable timer does a step. Time does not advance, and other timers with the same expiration time can then fire. If no timer is ready to fire, all timers increase (run) and non-deterministically, a step can occur (∃n, step(n)) or no step is done ( ( / 0) ∧ Ξ).

Transition Relation and Executions

The transition relation is a successor relation between states. It specifies that either a node makes a step (start or complete), or time advances but only if no timer node is ready to complete.

Transition Relation. Let s and s be two states. We say that s is a successor of s, iff the predicate Next(s, s ) (See equation. 1) holds. States, here s and s , correspond to tuples of the form (m e , m n , l c , g c ) and (m e , m n , l c , g c ), whose elements are used in the definitions of St and Ct.

Execution. An execution is an infinite sequence of states such that σ[0] is the initial state, and ∀i ∈ N, Next(σ[i], σ[i + 1]), where σ[i] denotes the i th state of the trace. Moreover, an execution is non-Zenon with regard to time and steps: there cannot be an infinite number of steps without time advancing, and there cannot be an infinite advancement of time without steps. Formally, the non-Zenon hypothesis corresponds to weak-fairness on the left-hand part of the Next disjunction, and to weak-fairness on its right-hand part. This ensures that if one node is enabled, it will eventually be done.

Encoding of the Semantics in Alloy

In this section, we present how Alloy has been used to implement our FOL semantics and verify timed BPMN models.

Alloy

Alloy is a declarative modelling language based on FOL and relational calculus for expressing complex structural and behavioral constraints [START_REF] Jackson | Software Abstractions: Logic, Language, and Analysis[END_REF]). Alloy's logic is quite generic and does not commit to a particular specification style [START_REF] Cunha | Bounded model checking of temporal formulas with alloy[END_REF]. We believe that this is more natural and allows preserving the expressiveness of the input modelling language, BPMN in our case. Alloy comes with a tool, Alloy Analyser, a constraint solver that provides automatic simulation and verification based on a model-finding approach using a SAT solver. Alloy has been used for the verification of UML Activity Diagrams [START_REF] Laurent | Formalization of fUML: An application to process verification[END_REF], in the Model-Driven Engineering domain [START_REF] Kleppe | MDA Explained: The Model Driven Architecture: Practice and Promise[END_REF], for the modelling and analysis of distributed system protocols [START_REF] Taghdiri | A lightweight formal analysis of a multicast key management scheme[END_REF], networks [START_REF] Georg | Using Alloy and UML/OCL to specify run-time configuration management: A case study[END_REF], and safety and security concerns in critical systems [START_REF] Dennis | Automating commutativity analysis at the design level[END_REF].

Implementation and Verification

Our semantics directly maps to Alloy which is also based on FOL. An element type (node or edge) is defined by an abstract signature, and the subtype relation relates these signatures (e.g., Node ⊇ Event ⊇ IntermediateEvent ⊇ T ICE ⊇ T ICE d ). A BPMN graph inhabits these signatures with unique elements that correspond to the graph nodes and edges. Attributes mark the endpoints of an edge.

Listing 1: An excerpt of the implementation of our semantics in Alloy. Next(s, s )

de f ≡ (Y = / 0 ∧   (∃n ∈ Y : step(n) ∧ f ztime(N Timer \ {n})) ∨ ∃n ∈ N EB , ∃eo ∈ out SF (n), (tgt(eo) ∈ Y ) ∧ step(n) ∧ f ztime(N Timer )   ∨ (Y = / 0 ∧ run() ∧ f ztime(N Timer \ S) ∧ ((∃n ∈ N : step(n)) ∨ ( ( / 0) ∧ Ξ))
(1) Two kinds of verification are available, checks on the structure itself, and checks on the executions. For the first kind, assertions ensure that the model is wellformed, e.g., a message flow connects two distinct processes. For the second kind, predicates on States are used to express properties on executions. We have defined :

• Safe, a predicate that states that no edge or node ever holds more than one token;

• SimpleTermination, a predicate that states that every process reaches a state where an End Event owns a token;

• CorrectTermination, a predicate that states that the whole system reaches a state where all processes have terminated with an End Event and no token are left on other nodes or edges.

• MaxTime, a predicate that states that the whole system reaches a final state before a given maximal time.

• MinTime, a predicate that states that the whole system takes at least a given minimal time to reach a final state.

Temporal constraints crossing the boundary of one process (e.g ., the deadline of message exchange), can be modelled in BPMN in two ways: (i) specify a latest date and time for the completion of a sending or receiving activity; this latter is modelled by associating a time boundary interrupting event to them (e.g, zone 1 in Fig. 2). (ii) specify receiving actions on different control flow depending on time limitation; this latter is modelled using an event based gateway followed by a timer catch event (e.g, zone 4 in Fig. 2) Current experiments have allowed to validate our semantics on a subset of study cases models, and the implementation proved the feasibility of our approach, but unfortunately real-life models are often out of reach of Alloy Analyzer as the number of required states for an execution exceeds its capacity.

Application Rule Example

To perform the verification, the process and the properties are translated into an Alloy specification. Then, this specification is given as input to the Alloy Analyzer which reduces the verification to a SAT problem.

To explain our approach with an example, consider Zone 1 in Fig. 2, an interrupting timer boundary event associated to the receive paper activity. As stated in Section.2, the start of an activity with timer boundary events causes the activation of the boundary events attached to it. If the specific fixed timedate defined on the boundary event is reached and the receive paper activity is still active, the boundary event interrupts the activity and generates a token on its outgoing edges. Fig. 3 shows a possible state which can be reached by the program. The configuration of this state is as follow: the PC chair process is active (R -1 (paperReview)=1), the global clock of the collaboration diagram reaches the timedate (2021-03-17 T 00:00), the receive activity review paper is active (m n (receivepaper)= 1) and there is no paper message in the communication channel (in MF (receivepaper) = 0). In this configuration; the interrupting timer boundary events completes, it drops the token from the receive paper activity (m n (receivepaper)= 0) and generates one on its outgoing edge (m e (out SF (tb1) = 1)).

Listing 2 presents the alloy implementation of the Boundary timeDate rule. The latter corresponds to the First Order Logic formula (6) presents in Table 3.

Listing 2: An excerpt of the implementation of the semantics of boundary event rule in Alloy.

RELATED WORK

Our paper focuses on the formalisation of BPMN time-related models that opens perspectives on quantitative analysis of business processes. This has been the subject of numerous works in the literature [START_REF] Wong | A relative timed semantics for BPMN[END_REF][START_REF] Morales | A formalization proposal of timed bpmn for compositional verification of business processes[END_REF][START_REF] Capel | Automating the transformation from BPMN models to CSP+ T specifications[END_REF][START_REF] Watahiki | Formal verification of business processes with temporal and resource constraints[END_REF][START_REF] Cheikhrouhou | Toward a time-centric modeling of business processes in BPMN 2.0[END_REF][START_REF] Cheikhrouhou | Toward a verification of time-centric business process models[END_REF][START_REF] Lanz | Process time patterns: A formal foundation[END_REF][START_REF] Combi | Modeling and handling duration constraints in BPMN 2.0[END_REF][START_REF] Combi | A modular approach to the specification and management of time duration constraints in BPMN[END_REF][START_REF] Durán | Verifying Timed BPMN Processes Using Maude[END_REF][START_REF] Durán | Stochastic analysis of BPMN with time in rewriting logic[END_REF].

In [START_REF] Wong | A relative timed semantics for BPMN[END_REF], the authors define a time-related semantics for BPMN when using relative time constraints. The approach presents an ab-stract syntax for BPMN, based on the Z notation and a semantics based on Communicating Sequential Processes (CSP). It handles the particular case of time durations.

In [START_REF] Morales | A formalization proposal of timed bpmn for compositional verification of business processes[END_REF][START_REF] Capel | Automating the transformation from BPMN models to CSP+ T specifications[END_REF], the authors propose an automated transformation from an extented version of BPMN 2.0 to timed CSP (CSP+T), as well as composition verification techniques for checking properties using the FDR2 model checker. They focus on the semantics proposed in [START_REF] Wong | A relative timed semantics for BPMN[END_REF].

In [START_REF] Watahiki | Formal verification of business processes with temporal and resource constraints[END_REF], the authors define a transformation approach for automatic generation of timed automata models from BPMN.

The works in [START_REF] Cheikhrouhou | Toward a time-centric modeling of business processes in BPMN 2.0[END_REF], [START_REF] Cheikhrouhou | Toward a verification of time-centric business process models[END_REF] address the need to model absolute and relative temporal constraints in timed automata. The authors extend BPMN models with a set of new notations to express temporal constraints, and then map timed business processes into timed automata.

In [START_REF] Combi | Modeling and handling duration constraints in BPMN 2.0[END_REF], the authors propose a formal specification of BPMN process diagrams based on time Petri nets. They model timer events of BPMN as transitions that have finite and positive temporal intervals. The authors represent a time duration as an interval, and they propose a mechanism for checking the duration constraints at run-time for the wellstructured BPMN regions. They extend their work, in [START_REF] Combi | A modular approach to the specification and management of time duration constraints in BPMN[END_REF], by specifying a set of duration models using directly BPMN elements, without extension, to capture duration constraints for the activities.

The authors of [START_REF] Durán | Verifying Timed BPMN Processes Using Maude[END_REF] present an approach for the formal verification and analysis of BPMN models. They propose an encoding of a subset of BPMN modelling elements into Maude where they introduce time duration and passing for tasks and flows. In this work they treat discrete (fixed) time duration. In [START_REF] Durán | Stochastic analysis of BPMN with time in rewriting logic[END_REF], they extend their work by associating stochastic expressions to the tasks and flows in order to represent timing behaviors and they associate probabilities for triggering outgoing flows in case of choice (i.e., exclusive and inclusive split gateways).

In [START_REF] Lanz | Time patterns for process-aware information systems[END_REF], the authors identify a set of time patterns to ease the comparison of process-aware information systems. The patterns are exhaustively analysed with respect to multiple design features. A formal semantics for the patterns, expressed as temporal execution traces, is given in [START_REF] Lanz | Process time patterns: A formal foundation[END_REF]. They implement a set of time pattern variants in the ATAPIS toolset. The latter maps a process schema to Conditional Simple Temporal Networks in order to 2 gives a synthetic comparison between these proposals and ours. The table focuses on (1) covering all the time events in BPMN, considering their categories, and (2) showing how these works support the presentation of time patterns. As far as the BPMN coverage criteria is concerned, we can observe that we are among the approaches with a high coverage. A few studies address the evaluation of BPMN expressiveness with respect to its modeling elements, and most of them extend the notation in order to enhance the support of the standard towards time management constraints [START_REF] Wong | A relative timed semantics for BPMN[END_REF], [START_REF] Morales | A formalization proposal of timed bpmn for compositional verification of business processes[END_REF][START_REF] Capel | Automating the transformation from BPMN models to CSP+ T specifications[END_REF], [START_REF] Watahiki | Formal verification of business processes with temporal and resource constraints[END_REF], [START_REF] Durán | Verifying Timed BPMN Processes Using Maude[END_REF], [START_REF] Durán | Stochastic analysis of BPMN with time in rewriting logic[END_REF].

As highlighted in Table 2, most of the existing works treat time duration for activities by extending BPMN by: (1) defining a non deterministic delay for a task [START_REF] Wong | A relative timed semantics for BPMN[END_REF] and [START_REF] Watahiki | Formal verification of business processes with temporal and resource constraints[END_REF] or, (2) representing a fixed duration a specified as an [a, a] interval [START_REF] Combi | Modeling and handling duration constraints in BPMN 2.0[END_REF]. However, BPMN gives the possibility to represent a duration for an activity using its own elements, without any extensions (see Fig. 4).

In addition, and to the best of our knowledge, no work in the literature allows one to specify the semantics for the different types of time information (i.e., date, cycle, duration) associated to BPMN timerelated events. In this paper we cover the defined set of BPMN timer events in their full generality. As an example, consider the timer boundary event with cycle type. BPMN defines the cycle type with reference to ISO standard definition, where the ISO cycle type definition represents a complex construct which may be a repetition based on a duration until date or a repetition defined by a starting date and a period, or others (Section 2). To the best of our knowledge, most papers do not support all the variations of this construct (see Table 2). However, some works (Camunda examples, 2020), limited by the absence of a formalization, propose a simplified version of these events, e.g. every 10 minutes (a repetition on a defined period).

Note that, even if the work in [START_REF] Lanz | Time patterns for process-aware information systems[END_REF]) provides a very rich formal semantics for process time pattern representation, it does not enable verification, and does not show their coverage w.r.t. standard BPMN elements.

CONCLUSION

We have proposed a formal semantics for the timerelated constructs of BPMN. This semantics supports different combinations of events, time information categories (date-times, durations, cycles) and the corresponding ISO-8601 descriptions as prescribed by the BPMN standard. It can be then used to give a semantics to BPMN models using Process Time Patterns [START_REF] Lanz | Workflow time patterns for process-aware information systems[END_REF][START_REF] Lanz | Time patterns for process-aware information systems[END_REF][START_REF] Lanz | Process time patterns: A formal foundation[END_REF]. Our proposal is based on a direct formalization in First Order Logic which we have then implemented in the Alloy input language, together with an extension of our fbpmn tool [START_REF] Houhou | A first-order logic semantics for communicationparametric BPMN collaborations[END_REF] to transform BPMN models into Alloy modules.

The Alloy implementation of our semantics is direct. Yet, one still has to find a better representation of time steps in it in order to make automated verification amenable. We plan here to study the use SATbased verification using Alloy Analyser in more case studies taking into account the execution time overage, max, min, waiting time synchronization, . . . ,etc. A longer term perspective concerns the support for data and conditional expressions over them through the use of a model checking modulo theories approach [START_REF] Calvanese | Formal modeling and SMT-based parameterized verification of data-aware BPMN[END_REF]. Further, we plan to experiment with a direct implementation of the semantics proposed herein into the SMT-lib input language to solve the verification issue.

n ∈ N T BE d St(n) de f ≡ ∃act ∈ N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ ( f time(n) timeValD = g c ) ∧ isInterrupt(n) ∧ ((act / ∈ N SP ∧ m n (act) = 0 ∧ (∀ee ∈ out SF (n), (m e (ee) = m e (ee) + 1)) ∧ ({act} ∪ out SF (n)) ∧ t ( / 0)) ∨ (act ∈ N SP ∧ ¬mayComplete(act) ∧ m n (act) = 0 ∧ (∀nn ∈ R(act) ∩ N, (m n (nn) = 0) ∧ (∀ee ∈ R(act) ∩ E, (m e (ee) = 0) ∧ (∀out ∈ out SF (n), (m e (out) = m e (out) + 1)) ∧ ({act} ∪ R(act) ∪ out SF (n)) ∧ t ( / 0))))) 5 n ∈ N T BE p St(n) de f ≡ ∃act ∈ N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ isInterrupt(n) ∧ ( f time(n) timeValP = l c (n)) ∧ (l c (n) = 0)) ∧ ((act / ∈ N SP ∧ (m n (act) = 0) ∧ (∀ee ∈ out SF (n), (m e (ee) = m e (ee) + 1)) ∧ ({act} ∪ out SF (n)) ∧ t ({n})) ∨ (act ∈ N SP ∧ ¬mayComplete(act) ∧ m n (act) = 0 ∧ (∀nn ∈ R(act) ∩ N, (m n (nn) = 0) ∧ (∀ee ∈ R(act) ∩ E, (m e (ee) = 0) ∧ (∀out ∈ out SF (n), (

Figure 1 :

 1 Figure 1: Subset of BPMN being taken into consideration in our work.

Figure 2 :

 2 Figure 2: Paper Reviewing case study.

  timeVal ): for example, if f time(n) = (T,V ), where T ∈ Ctime and V ∈ timeVal, then f time(n) Ctime = T , and f time(n) timeVal = V . Besides, when f time(n) Ctime = T cycle , then f time(n) timeVal = (r, d, p), with (r, d, p) ∈ Cycle. The projections timeVal R , timeVal P , and timeVal D give each element, with f time(n) timeVal R = r, f time(n) timeVal D = d and f time(n) timeVal P = p. Auxiliary functions. The following functions are defined: in/out : N → 2 E return the incoming/outgoing edges of a node, in(n) = {e ∈ E | tgt(e) = n} and out(n) = {e ∈ E | src(e) = n}. A family of functions in T (resp. out T

Figure 3 :

 3 Figure 3: Completion of an Interrupting Timer Boundary Event.

Figure 4 :

 4 Figure 4: Specifying activity duration (minimum , maximum).

≡

  m e (out) = m e (out) + 1)) ∧ ({act} ∪ R(act) ∪ out SF (n)) ∧ t ({n})))))6 n ∈ N T BE ⊕ d St(n) de f ≡ ∃act ∈ N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ ( f time(n) timeValD = g c ) ∧ ¬isInterrupt(n) ∧ (∀out ∈ out SF (n), (m e (out) = m e (out) + 1)) ∧ ({act} ∪ R(act) ∪ out SF (n)) ∧ t ( N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ (¬isInterrupt(n)) ∧ ( f time(n) timeValP = l c (n)) ∧ l c (n) = 0 ∧ (∀out ∈ out SF (n), (m e (out) = m e (out) + 1)) ∧ ({act} ∪ R(act) ∪ out SF (n)) ∧ t ({n}))))) N A , act = attachedTo(n) ∧ (m n (act) ≥ 1) ∧ (¬isInterrupt(n)) ∧ ( f time(n) timeValD = g c ) ∧ (rec(n) = f time(n) timeValR ) ∧ (l c (n) = 0) ∧ (l c (n) = 1) ∧ (rec (n) = rec(n) -1) ∧ (∀ee ∈ out SF (n), (m e (ee) = m e (ee) + 1)) ∧ (out SF (n)) ∧ t ({n})) Ct(n) de f ≡ ∃act ∈ N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ (¬isInterrupt(n)) ∧ (rec(n) = f time(n) timeValR ) ∧ (rec(n) = 0) ∧ ( f time(n) timeValP = l c (n)) ∧ (l c (n) = 1) ∧ (rec (n) = rec(n) -1) ∧ (∀ee ∈ out SF (n), (m e (ee) = m e (ee) + 1)) ∧ (out SF (n)) ∧ t ({n}) N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ (¬isInterrupt(n)) ∧ ( f time(n) timeValD = g c ) ∧ ( f time(n) timeValP = l c (n)) ∧ (rec (n) = rec(n) -1) ∧ (l c (n) = 1) ∧ (∀ee ∈ out SF (n), (m e (ee) = m e (ee) + 1)) ∧ (out SF (n)) ∧ t ({n})) N A , (act = attachedTo(n)) ∧ (m n (act) ≥ 1) ∧ (¬isInterrupt(n)) ∧ ( f time(n) timeValP = l c (n)) ∧ (rec (n) = rec(n) -1) ∧ (l c (n) = 1) ∧ (∀ee ∈ out SF (n), (m e (ee) = m e (ee) + 1)) ∧ (out SF (n)) ∧ t ({n})) ∈ in SF (n), (m e (e)≥1) ∧ (m e (e) = m e (e) -1) ∧ ∃e ∈ out SF (n), tgt(e ) ∈ N {RT,CMIE} ∧ ∃m f ∈ in MF (tgt(e )), (m e (m f ) ≥ 1) ∨ tgt(e ) ∈ N T ICEp ∧ (l c (tgt(e )) ≥ f time timeValP (tgt(e ))) ∨ tgt(e ) ∈ N T ICE d ∧ (g c ≥ f time timeValD (tgt(e ))) ∧ (m e (e ) = m e (e ) + 1) ∧ ({e, e }) ∧ t ({}) in SF (n), (m e (e) ≥ 1) ∧ (m e (e) = m e (e) -1) ∧(m n (n) = m n (n) + 1) ∧ (∀te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) ,T BE p } , (n = attachedTo(te)) ∧ (l c (n) = 0) ⇒ (l c (n) = 1)) ∧ ({n, e}) ∧ t ({te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) ,T BE p } | (n = attachedTo(te)(m n (n) ≥ 1) ∧ (m n (n) = m n (n) -1) ∧ (∀e ∈ out SF (n), (m e (e) = m e (e) + 1)) ∧ (∀te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) } , (n = attachedTo(te)) ⇒ (l c (n) = 0)) ∧ ({n} ∪ out SF (n)) ∧ t ({te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) } | (n = attachedTo(te)in SF (n), (m e (e) ≥ 1) ∧ (m e (e) = m e (e) -1) ∧ (m n (n) = m n (n) + 1) ∧ (∀n se ∈ (N T SE ∩ R(n)), (m n (n se ) = m n (n se ) + 1)) ∧ (∀te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) ,T BE p } , (n = attachedTo(te)) ⇒ (l c (n) = 1)) ∧ ({e, n} ∪ (N T SE ∩ R(n))) ∧ t ({te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) ,T BE p } | (n = attachedTo(te))}) Ct(n) de f ≡ (m n (n) ≥ 1) ∧ (m n (n) = 0) ∧ (∀e ∈ R(n) ∩ E, (m e (e) = 0)) ∧ (∃n ee ∈ (N EE ∩ R(n)), (m n (n ee ) ≥ 1)) ∧ (∀nn ∈ R(n) ∩ N, (m n (nn) ≥ 1 ⇒ nn ∈ N EE )) ∧ (∀nn ∈ (R(n) ∩ N EE ), (m n (nn) =0)) ∧ (∀e ∈ out SF (n), (m e (e) = m e (e) + 1)) ∧ (∀te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) } , (n = attachedTo(te)) ⇒ (l c (te) = 0)) ∧ ({n} ∪ (R(n) ∩ N EE ) ∪ out SF (n)) ∧ t ({te ∈ N {T BE ⊕ p ,T BE ⊕ c(p) ,T BE ⊕ c(end) } | (n = attachedTo(te))})

Table 1 :

 1 Time-related features in BPMN and their relation to ISO-8601, support: BPMN and us (•), BPMN only (•).

	TimerEventDefinition		BPMN Standard ISO-8601	TSE TICE	TBE Interrupt non-Interrupt TBE
	timeDate	date and time yyyy-mm-ddThh:mm:ssZ	•	•	•	•
			R/ yyyy-mm-ddThh:mm:ssZ / yyyy-mm-ddThh:mm:ssZ	•	•	-	•
		unbounded	R/ yyyy-mm-ddThh:mm:ssZ / PnYnMnDTnHnMnS R/ PnYnMnDTnHnMnS/yyyy-mm-ddThh:mm:ssZ	• •	• •	--	• •
	timeCycle		R/PnYnMnDTnHnMnS Rn/ yyyy-mm-ddThh:mm:ssZ/yyyy-mm-ddThh:mm:ssZ	• •	• •	--	• •
		bounded	Rn/ yyyy-mm-ddThh:mm:ssZ/PnYnMnDTnHnMnS Rn/ PnYnMnDTnHnMnS/yyyy-mm-ddThh:mm:ssZ	• •	• •	--	• •
			Rn/ PnYnMnDTnHnMnS	•	•	-	•
	timeDuration	duration	PnYnMnDTnHnMnS	-	•	•	•

  a date (and time) expressed in seconds with respect to a reference date (1970-01-01T00:00:00Z). Date refers to the timeDate of the BPMN standard. A date like 2020-12-M is the set of message types, • cat N : N → T Nodes gives the type of a node,

03T13:52:33Z in ISO-8601 format is converted to 1, 607, 003, 553 seconds. • Duration ⊆ N represents a time duration in seconds. This corresponds to the timeDuration of the BPMN standard. A P3DT15M duration in ISO-8601 format (3 days and 15 minutes) is converted to 259, 215 seconds. Note that we do not support years and months in durations due to the ambiguity of their correspondence in seconds. • Cycle = (N ∪ {ι}) × [Duration ∪ (Date × Duration) ∪ (Duration × Date)], represents a composite timing type. It defines time redundancies along with a time duration, a fixed start date and time duration, or a time duration and a fixed end date. The number of repetitions is either bounded or not (ι).

Definition 1. BPMN Graph. (extended from

[START_REF] Houhou | A first-order logic semantics for communicationparametric BPMN collaborations[END_REF]

)) Given T Nodes ,T Edges A BPMN graph is a tuple G= (N, E, M, cat N , cat E , src, tgt, R, msg t , attachedTo, isInterrupt, f time) such that:

• N is the set of nodes,

• E (N ∩ E = / 0) is the set of edges, •

Table 2 :

 2 Comparison between approaches supporting BPMN time-constructs. Table

In T ICE p , p stands for period as in the ISO-8601 standard for durations.

Acknowledgements. This work was supported by project PARDI ANR-16-CE25-0006.

reference [START_REF] Wong | A relative timed semantics for BPMN[END_REF]) [START_REF] Morales | A formalization proposal of timed bpmn for compositional verification of business processes[END_REF]) [START_REF] Watahiki | Formal verification of business processes with temporal and resource constraints[END_REF] [START_REF] Cheikhrouhou | Toward a time-centric modeling of business processes in BPMN 2.0[END_REF] [START_REF] Lanz | Process time patterns: A formal foundation[END_REF] [START_REF] Combi | Modeling and handling duration constraints in BPMN 2.0[END_REF] [START_REF] Durán | Verifying Timed BPMN Processes Using Maude[END_REF] ours [START_REF] Capel | Automating the transformation from BPMN models to CSP+ T specifications[END_REF] (

check the temporal consistency of process schema at design time, and check time violations at runtime. Some works focus on extending the BPMN notation to capture temporal perspectives such as [START_REF] Gagné | Time-bpmn[END_REF]. This work presents a classification of flexible and inflexible temporal constraints (e.g. As Soon as Possible and As Late as Possible) and temporal dependencies between activities. Discussion. The authors of [START_REF] Lanz | Workflow time patterns for process-aware information systems[END_REF] define ten process time patterns suitable for evaluating the support of the temporal perspective in processaware information systems (PAISs). According to APPENDIX Table 3: An excerpt of BPMN semantic rules.

Rule

Node Formulas


Erick Cardoso Costa
email: erick.cardoso.costa@posgrad.ufsc.br

Fabio Antonio Xavier

Ricardo Knoblauch

Cristiano Binder

Walter Lindolfo Weingaertner

Effect of cutting parameters on surface integrity of monocrystalline silicon sawn with an endless diamond wire saw

Keywords:

The cutting of silicon wafers using multi-diamond wire sawing is a critical stage in solar cell manufacturing due to brittleness of silicon. Improving the cutting process output requires an in-depth understanding of phenomena associated with cutting parameters. In order to investigate the influence of diamond wire sawing on surface integrity of monocrystalline silicon, a looped diamond wire was used and cutting parameters wire cutting speed, feed rate and wire tension were varied. The surface morphology was observed by scanning electron microscopy. Surface roughness S a was measured with a non-contact profilometer. The brittle-ductile transition was identified by presence of residual phases on sawn surface. A bevel-polishing method was employed to determine the microcrack depth. The results show that with higher feed rate the surface presents deeper and wider craters because of deeper penetration of diamond grain. On increasing wire cutting speed, there were more regions formed in ductile mode. The higher S a values was observed on increasing both feed rate and wire tension, while S a decreased with an increase in wire cutting speed. The brittle mode was predominant with an increase in feed rate, resulting in Si-I phase in regions formed in fragile mode. Material removal in ductile mode led to appearance of a-Si phase at high wire cutting speed. No significant effect was observed on increasing wire tension. Subsurface microcracks mainly initiating from bottom of grooves generated by cutting mechanism. The most appropriate set of cutting parameters is the lowest feed rate and wire tension and highest wire cutting speed.

Introduction

Crystalline silicon is the main material used for manufacturing solar cells in the photovoltaic industry, with around 95% of the solar cells manufactured being based on this material (62% multi-crystalline silicon and 33% monocrystalline silicon). Consequently, the photovoltaic industry consumes approximately 90% of the crystalline silicon produced globally. Crystalline silicon is favored over other semiconductor materials due to its abundance in the earth's crust, comprising approximately 27% of the minerals present (Ozturk et al., 2018a;[START_REF] Yu | Thin Czochralski silicon solar cells based on diamond wire sawing technology[END_REF]. The semiconductor characteristics of crystalline silicon allows a high efficiency to be obtained in power generation.

In order to produce solar cells, crystalline silicon ingots are sawn into wafers with a thickness of 100-180 μm. Currently, the reciprocating multi-wire sawing (MWS) process is almost exclusively employed in the photovoltaic industry to cut hundreds, and even more than one thousand, wafers from a single crystalline silicon ingot [START_REF] Möller | Wafer processing[END_REF]. The MWS processes are divided in multi-wire slurry sawing (MWSS) and multi-wire diamond wire sawing (MWDWS). MWSS is a free-abrasive machining method, referred to as the threebody wear mechanism. The cut is performed by a loose silicon carbide (SiC) abrasive dispersed in polyethylene glycol, which is supplied through nozzles over a wire web and carried by gravity to the wire in the sawing channel. MWDWS is performed through a two-body wear mechanism through the interaction of the bonded diamonds on the abrasive wire with the workpiece. MWDWS is widely applied for slicing brittle-hard materials, such as crystalline silicon, sapphire crystals, SiC, stones and optical glass [START_REF] Gao | Experiment study on electroplated diamond wire saw slicing single-crystal silicon[END_REF][START_REF] Wu | Wire sawing technology: A state-of-the-art review[END_REF].

Although both sawing processes are widely used in the industrial sector, MWDWS has some advantages over MWSS, including higher material removal rate, better surface quality and, if correctly used, lower machining cost per wafer [START_REF] Chen | Novel texturing process for diamondwire-sawn single-crystalline silicon solar cell[END_REF]Liu et al., 2017a).

However, the residual damage introduced by the sawing process, which includes surface roughness, phase transformation and microcracks, remains unavoidable and directly affects the main mechanical, optical and electronic properties of the crystalline silicon wafer (Liu et al., 2017a). Due to the manufacturing of thinner and larger silicon wafers, the damage to the surface integrity, mainly in the form of subsurface microcracks, decreases considerably the fracture strength of the sliced silicon wafer during the post-processing step (e.g., lapping and polishing) as well as the lifespan of the solar module (Liu et al., 2017b;Ozturk et al., 2018b). This generates some concern given that MWDWS is a critical process in the solar cell production chain.

Strategies adopted to reduce the damage at the surface and subsurface of monocrystalline silicon (mono-Si) wafers are associated with the applied cutting conditions, such as wire cutting speed (v c ), feed rate (v f ) and wire tension (T wire ), as well as the characteristics of the wire [START_REF] Kumar | Effect of wear of diamond wire on surface morphology, roughness and subsurface damage of silicon wafers[END_REF]. Many researchers have been trying to understand the macro and micro-kinematics of the sawing process by means of mathematical models and experimental approaches. In the literature, experiments carried on MWDWS are not described in depth. Most researchers have focused on single-diamond wire sawing (DWS). Regarding the surface integrity, [START_REF] Gao | Experiment study on electroplated diamond wire saw slicing single-crystal silicon[END_REF] investigated the influence of the cutting parameters (v c ≤ 2 m/s; v f ≤ 0.75 mm/min) and different cutting fluids on the surface topography, surface roughness, subsurface damage, total thickness variation and bending of the sawn mono-Si. Liu et al. (2017a) evaluated the subsurface microcrack damage of mono-Si induced by DWS with different cutting parameters (v c ≤ 1.5 m/s; v f ≤ 0.75 mm/min). The authors formulated a mathematical model to describe the microcrack formation based on fracture mechanics theory. Their experimental results validated the proposed model and showed that the depth of the microcracks is mainly influenced by both cutting parameters v c and v f . [START_REF] Gao | Material removal and surface generation mechanisms in diamond wire sawing of silicon crystal. 104642[END_REF] carried out experiments to analyze the influence of the v f /v c ratio on the brittle-ductile transition in the DWS of mono-Si. On evaluating different cutting parameters (v f ≤ 0.75 mm/min; v c ≤ 2 m/s) they observed that the v f /v c ratio has a significant influence on the material removal mechanism. [START_REF] Pala | Characterization of electroplated diamond wires and the resulting workpiece quality in silicon sawing[END_REF] introduced a method for the characterization of the surface morphology by image processing and they showed that both v c and v f influence the percentage of ductility and fragility of the sawn surface of mono-Si. However, the authors carried out experiments employing kinematics similar to that of grinding and the material removal mechanism was not validated by the residual crystalline phase. [START_REF] Kayabasi | Determination of cutting parameters for silicon wafer with a Diamond Wire Saw using an artificial neural network. Sol. Fig. 11. Influence of the cutting parameters on the subsurface microcrack depth[END_REF] investigated the effects of variations in the wire cutting speed (v c ≤ 4.5 m/s), feed rate (v f ≤ 2 mm/min) and oil/water emulsion ratio (100% and 30% oil) on the surface roughness of sawn mono-Si wafers. An artificial neural network (ANN) was accommodated to predict the surface roughness parameter R a using the data obtained from the DWS cutting experiments. Ozturk et al. (2018b) used regression models to optimize the surface roughness (parameters R a , R q and R z ) of mono-Si specimens cut with a diamond wire. They employed a wire cutting speed of v c ≤ 4.5 m/s and feed rate of v f ≤ 1 mm/min.

The aforementioned authors provided valuable results, but an effective correlation between the cutting parameters and surface integrity of mono-Si wafers cut by DWS has not yet been established. Furthermore, the wire cutting speed of v c = 20 m/s is widely employed in the wafering industry; however, few experiments have been conducted using a wire cutting speed close that value. [START_REF] Kumar | Effect of wear of diamond wire on surface morphology, roughness and subsurface damage of silicon wafers[END_REF] analyzed the wear of diamond wires for a wire cutting speed of v c = 18 m/s. [START_REF] Knoblauch | Investigation of the progressive wear of individual diamond grains in wire used to cut monocrystalline silicon[END_REF] carried out experiments using an endless wire saw test rig to analyze the progression of wear in the diamond sawing of mono-Si, with a wire cutting speed of v c = 13.7 m/s and constant feed force of F f = 3.1 ± 0.6 N. [START_REF] Suzuki | Mechanisms of material removal and subsurface damage in fixed-abrasive diamond wire slicing of single-crystalline silicon[END_REF] investigated the effect of the diamond grain size and number of sawing cycles on the surface roughness and subsurface damage using a wire cutting speed of v c = 29 m/s. However, although these authors applied wire cutting speeds close to those used in industrial applications, the influence of the cutting conditions on the surface integrity was not evaluated. A previous investigation revealed that there is a close relationship between the microcrack depth and surface roughness in terms of the parameter R z , and that the surface and subsurface integrity is strongly influenced by variations in the cutting parameters when silicon is cut using the diamond wire sawing process [START_REF] Costa | Influence of diamond wire sawing parameters on subsurface microcracks formation in monocrystalline silicon wafer[END_REF].

In order to contribute to the diamond wire sawing (DWS) technology and better understanding the material removal phenomena involved in the sawing of mono-Si wafers, the effects of the main cutting parameters (v c , v f and T wire ) on the surface integrity of sawn mono-Si workpieces were investigated. This paper reports an experimental study on the characteristic of the brittle-ductile transition of the sawn surface of mono-Si and discusses the results considering the surface morphology, surface roughness, phase transformation and microcracks in the subsurface region. The present paper is an important study for the researches aiming directly increase the silicon wafer quality in photovoltaic applications.

Experimental procedure

Experimental setup and design of experiments

The experiments were carried out on the endless wire saw developed by Knoblauch et al. (2017a), shown in Fig. 1. In contrast to the industrial DWS machines, in this study a single-electroplated diamond wire in the shape of a loop was employed. Thus, instead of using a few thousand meters of wire for a multi-cut, single cuts were performed using only around a 1-meter segment of diamond wire. The ends of the industrial diamond wire segment were butt-welded on a welding device developed by Knoblauch et al. (2017b). After the loop shape had been obtained, the diamond wire was wrapped around two Teflon® discs and moved by the driven rotary axis with constant rotation to perform the cut with a constant wire cutting speed (v c ).

The test rig slides and rotatory bearings (X, Y, Z, a and a′) are based on aerostatic slides/bearings, which ensure low friction on them (see Fig. 1). This ensures that the applied forces are correspondingly applied in the cutting zone (no stick-slip effect on the input variables) and allows the cuts to be controlled with constant wire tension. The cut is performed by the endless diamond wire wrapped around two Teflon® pulleys, mounted on the front side of the two rotatory spindles. An electric AC motor, controlled by a frequency inverter, drives the main spindle. The maximum cutting speed of the wire is v c = 26 m/s. The wire tension (T wire ) is set by the air pressure on a pneumatic cylinder and controlled by the deflection of a spiral spring. The vertical feed movement is driven by a step motor/ball bearing system. The minimum feed rate is v f = 0.08 mm/min and the value can be set using the control interface. The width of the mono-Si specimen slices is manually set on the Z-axis by a micrometer adjustment screw.

The diamond wire used in this study is an industrial Ni electroplated diamond wire, manufactured by Norton Saint-Gobain Abrasives, with an outer diameter Ø OD = 350 µm, wire core diameter of 250 μm and diamond grain size of 30-45 μm. The diamond grains are distributed randomly over the wire surface and bonded by a nickel (Ni) layer (Fig. 2).

Considering its widespread use in the manufacturing of solar cells, mono-Si was employed for this study, in the form of rectangular test specimens with dimensions of 25 mm × 50 mm × 7 mm (Fig. 3a). The specimens were sawn into slices (25 mm × 1 mm × 7 mm) with 1 mm thickness, parallel to the crystallographic plane (100), according to the Miller index (see Fig. 3b). The cutting direction in the kerf is normal to the crystallographic plane (010).

A full factorial design of experiments (DOE) was performed and experiments were carried out using the cutting parameters v c and v f at three different levels (low, medium and high), and T wire at two levels (low and high), as indicated in Table 1. Each experiment was performed three times.

For each single sawing experiment, a new (unworn) diamond wire was employed to minimize the effect of the wear of the diamond wire on the workpiece surface integrity. The cuts were performed dry. The sawn specimens were submitted to surface integrity analysis, based on the following techniques: surface morphology analysis by scanning electron microscopy (SEM), surface roughness analysis, micro-Raman spectroscopy and subsurface damage analysis (details are given in Section 2.2).

A statistical evaluation was carried out to quantify the influence of the cutting parameters v c , v f and T wire on the surface integrity. Analysis of variance (ANOVA), with a 95% confidence interval and confidence level of α = 0.05, was performed to determine the effects of the factors, the divergence percentages and the p-values, as described by [START_REF] Montgomery | Applied Statistics and Probalisty for Engineers[END_REF].

Surface integrity analysis

Surface morphology

The surface morphology characteristics of the mono-Si specimens, sawn applying different cutting parameters, were determined by SEM (Hitachi TM-3030 microscope). The SEM micrographs allow the damage caused to the surface by the sawing process to be observed, which provides information on the material removal mechanisms that act during the cutting process.

Surface roughness

The surface roughness of the sawn specimens is influenced by the characteristics of the diamond wire and the distribution of the diamond grains on the wire. Therefore, the surface roughness was measured using an optical non-contact profilometer (Zygo NewView 7300). Three-dimensional images of the surface topography were generated using the software MetroPro®, version 8.1.5. For each sawn specimen, images of three different regions, with an area of 1 mm 2 , were acquired in order to obtain an average value for the measured surface roughness. The software MountainsMap Universal® 7.1 was used to process the measurement data, as recommended in ISO 16610-61, and the surface roughness parameter S a (arithmetic average height) was extracted according to ISO 25178-2. As a result, for the three specimens sawn under the same cutting conditions, an arithmetic mean value of S a was determined.

Raman spectroscopy

Raman spectroscopy was used to identify the presence of different crystalline phases on the sawn surface. The sawn specimens were analyzed using a Renishaw® inVia micro-Raman microscope that operates with an Ar-laser (wavelength of 514.2 nm). The focal point of the laser was set on the sawn surface with an optical magnification lens (500x), and the Raman spectra were acquired through an accumulation of 10 s with three replicates in the bandwidth region of 200-700 cm -1 using the software Wire3.4®.

Based on considerations made by [START_REF] Gao | Material removal and surface generation mechanisms in diamond wire sawing of silicon crystal. 104642[END_REF] regarding the influence of the r-ratio v f /v c (dimensionless) on the material removal mechanism in DWS, four mono-Si specimens sawn with different r-ratios were analyzed. In each case, the analysis was performed twice and the two regions investigated showed evidence of (i) the brittle mode and (ii) the ductile mode of material removal. This step was carried out in order to confirm the presence of brittle material removal and the progression of ductile material removal in the region by detecting the residual crystalline phases on the sawn surface corresponding to each material removal mechanism.

Subsurface damage

Based on the ASTM F 950-02 standard, an embedding and bevelpolishing method was employed to analyze the depth of subsurface damage caused by the cutting of mono-Si specimens (see Fig. 4). The mono-Si specimens sawn by DWS were embedded in acrylic resin with a tilt angle α (°), after being ground and polished. The depth of the microcrack damage observed on the polished surface was obtained under the bevel angle α, which permitted the geometric determination of the arithmetic mean depth of the microcracks for each specimen analyzed.

Results and discussion

Surface morphology

Figs. 5 and6 shows the SEM micrographs of the sawn surface of the mono-Si specimens cut with a wire tension of T wire = 20 N and T wire = 30 N, respectively. The sawn surfaces are composed of parallel and oriented grooves that follow the direction of the effective sawing movement, as also noted by [START_REF] Bidiville | Diamond wire-sawn silicon wafersfrom the lab to the cell production[END_REF] and [START_REF] Yu | Thin Czochralski silicon solar cells based on diamond wire sawing technology[END_REF]. Each SEM image shows areas with craters, microcracks and pitting, which are formed under the fragile (brittle) regime, and smooth areas characterized by the presence of parallel and oriented grooves, formed under the ductile regime. On comparing the nine cutting conditions evaluated for each T wire , it can be observed that the proportion of each cutting regime varies with a variation in the cutting parameters (v c and v f ). This is in agreement with the results of [START_REF] Gao | Material removal and surface generation mechanisms in diamond wire sawing of silicon crystal. 104642[END_REF], although the respective values of v c and v f were much lower than the parameters used in this study.

On applying a high v f , the material removal occurs predominately through the fragile regime. Due to the penetration of the most protruded diamond grains into the mono-Si surface, corresponding to a high average undeformed chip thicknesses (h cu ), on exceeding a critical value (h cu,crit ), plastic deformation gives way to microcrack formation and propagation. A further increase in v f induces surface formation predominantly with fragile fracture as the main material removal mechanism. According to Liu et al. (2017b), an increase in v f leads to a higher number of active diamond grains that effectively are assuming the cut, with material removed under the brittle regime, and this situation progresses with increasing v f while maintaining v c and T wire constant.

On the other hand, increasing v c , while maintaining the same conditions described for the variation in v f and T wire , resulted in a reduction in the microcracks and craters on the sawn surface. The diamond grains present different degrees of protrusion and their shapes vary, which leads to a difference in the stress state acting at point of grain/material contact. As a consequence, the sawn surface presents regions with evidence of mixed ductile and fragile modes, as seen in the SEM micrographs in Figs. 5 and6. Considering a fixed range of diamond grain protrusion and that all diamond grains are in contact with the surface of the mono-Si specimen, an increase in v c would increase the engagement frequency of the diamond grains on the mono-Si specimen along the sawing line, leading to a decrease in h cu . As a result, more kinematic cutting edges will engage and contribute to the removal of ductile material, as reported by Liu et al. (2017b) and [START_REF] Chung | Depth of cut per abrasive in fixed diamond wire sawing[END_REF]. This change from brittle to ductile mode in the material removal mechanism, resulting in surfaces with more regions that are free of fractures associated with the fragile mode.

All sawn surfaces obtained in these experiments exhibited both ductile and fragile material removal modes. The ductile regime was dominant for the combination of highest v c and lowest v f . On comparing the results in Figs. 5 and6, although the wire tension increases, the sawn surfaces under both wire tension conditions presented similar morphological characteristics, indicating a mixture of fragile and ductile modes as the material removal mechanism. However, the fragile behavior observed in the SEM micrographs in Fig. 5 is slightly more accentuated when the T wire is increased from 20 to 30 N, as can be seen in Fig. 6.

Surface roughness

The surface roughness is influenced by variations in v f , v c and T wire . Fig. 7 shows the results for the variation in the arithmetic mean value for the surface roughness parameter S a for the mono-Si specimens sawn under different cutting conditions. It can be observed that the mean value increases with an increase in v f and decreases with high v c , for both T wire values. This can be explained by the combination of brittle/ ductile regimes during the chip formation. At high v f and low v c the sawn surface is formed by extensive fractured regions, observed in the form of craters [START_REF] Jackson | Machining with Abrasives, Machining with Abrasives[END_REF]. According to [START_REF] Klocke | Manufacturing Process 2: Grinding, Honing, Lapping, RWTH[END_REF], fragile fractures can be attributed to an increase in the frictional force per grain and, consequently, higher h cu due to an increase in the penetration of the diamond grains. Therefore, as described by [START_REF] Bifano | Ductile-regime grinding: a new technology for machining brittle materials[END_REF], the penetration depth has a significant influence on the fragile fracture formation, resulting in the presence of more craters and pitting on the sawn surface.

The graphs in Fig. 7 show that the surface roughness parameter S a presented a slight reduction with an increase in v c from 10 to 20 m/s. According to [START_REF] Marinescu | Handbook of Ceramics Grinding and Polishing, 1st ed, Handbook of Ceramics Grinding and Polishing[END_REF], this behavior is associated with a reduction in h cu as a consequence of the higher engagement frequency of the diamond grains on surface of the specimen. A lower penetration depth of the grains favors material removal in the ductile regime, reducing the surface roughness, since more damage-free regions are generated during the surface formation.

Higher S a values were obtained for the highest v f and lowest v c for both wire tensions, as seen in Fig. 7a and7b. An increase in T wire caused an increase in the surface roughness with notably higher values of S a . An increase in the wire tension from 20 to 30 N reduced significantly the wire deflection during the cutting process. Considering the kinematics of the cutting process shown schematically in Fig. 8, it can be seen that in the initial stage (see Fig. 8a) there is no contact between the wire and the specimen, and the cutting wire movement remains perpendicular to the feed rate (v f ). With the feed movement of the specimen against the wire, a deflection effect was observed, as shown in Fig. 8b. Although the chip removal mechanism of the diamond wire sawing is similar to that of the grinding process, the diamond wire is considered a flexible cutting tool. This characteristic generates a displacement of the free wire length in the form of a wire bow with an angle (Φ). In comparison to the initial stage (Stage 1), the diamond wire will then be in a new vertical position (Stage 2) caused by its deflection, as shown in Fig. 8c.

Applying a wire tension T 2 > T 1 , for same condition of v c and v f , result in an angle Φ 2 smaller than the wire bow angle (Φ 1 ) generated under a wire tension T 1 , as shown in Fig. 8d. In the experiment was observed that an increase in T wire from 20 to 30 N reduces the deflection effect and the wire bow angle (Φ) becomes smaller, resisting the force perpendicular to the cutting movement direction (component of feed force). As a results, there is a significant increase in the material removal rate due to the higher h cu , compared to that at T wire = 20 N. In this regard, it can be stated that the higher material removal rate is the main factor that led to higher S a values when the T wire was varied from 20 to 30 N.

The behavior of the parameter S a obtained from the surface roughness measurements (see Fig. 7) are consistent with the surface According to the ANOVA analysis, an increase in v c decreased the surface roughness parameter S a by up to 10.2% (p-value = 0.000894). On the other hand, there was an increase in the S a values on increasing both cutting parameters v f and T wire . With an increase in v f , the value of S a increased by up to 15.6% (p-value = 0.000003). In the case of T wire , an increase from 20 to 30 N resulted in an increase in the S a values by up to 34.3% (p-value = 0.000000). Based on the ANOVA results, it can be stated that variations in the cutting parameters v c , v f and T wire had a significant effect on the surface roughness of the mono-Si specimens, since the p-values remained at < 0.05 for all factors analyzed.

Raman spectroscopy

The SEM micrographs on the left side of Fig. 9 show the regions analyzed by Raman spectroscopy for the specimens sawn applying different cutting conditions, considering the r-ratio (v f /v c ). The image in Fig. 9a shows a surface composed of extensive and deep craters, which indicates that there was a predominance of the fragile regime as the material removal mechanism. According to [START_REF] Bifano | Ductile-regime grinding: a new technology for machining brittle materials[END_REF], this characteristic suggests that h cu exceeded h cu,crit , which means that the fracture resistance limit is reached before plastic deformation occurs, resulting in the material removal by fragile fracture. Therefore, the surface was formed through crack propagation resulting in the presence of craters on the sawn surface. The analysis of the phase transformation was based on the Raman spectra for the sawn surfaces, also shown in Fig. 9. The spectra in Fig. 9a show a single peak at 523 cm -1 , corresponding to the cubic diamond phase structure (Si-I). According to [START_REF] Wu | Effect of crystallographic orientation on ductile scribing of crystalline silicon: Role of phase transformation and slip[END_REF], the Si-I phase is present in regions where the material removal mechanism was predominantly the fragile regime. Therefore, as the chip formation and removal was mainly by crack propagation, the pure crystal silicon (Si-I phase) becomes exposed.

The sawn surfaces shown in Fig. 9b also exhibit a predominance of the fragile regime, evidenced by craters and a few damage-free spots.

The Raman spectra in Fig. 9b show three new peaks at 349 cm -1 (Si-XII phase), 433 cm -1 (Si-III phase), and 469 cm -1 (a-Si phase). The plasticity of the crystalline silicon have as primary mechanism the highpressure phase transformation that cause brittle-ductile transition. The presence of these residual crystalline phases suggests that the Si-I phase underwent a phase transformation to the metallic phase Si-II due to the action of the grain/material contact pressure, which permits plastic deformation during chip formation. This is a result of the increase in v c from 10 m/s to 15 m/s, which induces a lower h cu value due to the highest engagement frequency of the diamond grain on the surface of the mono-Si. It can be stated that a value of v c = 15 m/s allows the phase transformation of Si-I to metastable Si-II which can assume the crystalline and amorphous phases. The residual phases observed are formed by different unloading conditions: Si-XII and Si-III phases are attributed to a slow unloading rate and the a-Si phase is a result of a high unloading rate. These results can be attributed to the different levels of protrusion and shapes of the diamond grain, which lead to variations in the stress states underneath the grain/material contact point. Although there are different residual phases, the Si-XII, Si-III and a-Si phases occur due to the shear-induced phase transformation of the mono-Si during chip removal in the ductile regime.

The SEM micrographs in Fig. 9c and9d show the sawn surface of the mono-Si specimen obtained with r-ratios of 2.5 × 10 -5 and 1.6 × 10 -5 , respectively. The characteristic predominance of a smooth surface can be observed with oriented, parallel and damage-free grooves, the socalled saw mark grooves. This suggests that on increasing v c and decreasing v f the mono-Si cutting occurs predominantly in the ductile regime, although the a few regions with craters are still presented, which indicates that part of the material was removed in the fragile regime due to different degrees of protrusion and shape of the diamond grains as well as lateral vibrations of the diamond wire.

The damage-free grooves correspond to the material removal mechanism in the ductile regime, as can be observed by the appearance of a secondary phase of silicon due to the phase transformation phenomenon. This phase transformation from Si-I to Si-II with β-tin structure at high-pressure phase transformation results in the formation of an amorphous and metastable phase, which is a consequence of the ductile behavior of the mono-Si during plastic deformation. Under the ductile cutting conditions, it is possible to avoid microcrack initiation, since the mono-Si behaves as a ductile material during chip formation and removal. This is evidenced by the Raman spectra in Fig. 9c and9d, where the bandwidth of the amorphous phase (a-Si) has a peak at 475 cm -1 . The presence of the a-Si phase is consistent with the ductile removal of mono-Si during the cutting, which is caused by grains that cut with h cu below the critical value (h cu,crit ) that produce a microcutting as well as by grains that are only generates ploughing over the workpiece surface. [START_REF] Wang | Effect of scratching speed on phase transformations in high-speed scratching of monocrystalline silicon[END_REF] reported that the phase transformation of the (100) mono-Si during high-speed scratching shows several residual phases as a consequence of the ductile mode of the material. The authors evidenced that at high-speed scratching between 10 m/s and 25 m/s there is an exponential increase in the intensity of the a-Si and Si-IV peaks on the Raman spectra, caused mainly by a higher unloading rate. Based on this finding, along with the results obtained during the mono-Si cutting by diamond wire sawing experiments, it can be stated that v c = 10 m/s is the threshold for the phase transformation, and an increase in v c generates a more intense phase transformation, which leads to the amorphization of the silicon. In this regard, an increase in v c (10, 15 and 20 m/s) results in a sawn surface with a greater presence of residual phases, which indicates the ductile removal mode for the mono-Si chips. This can be seen in Fig. 9 (a, b, c andd), where the bandwidth and intensity of the a-Si phase observed on the Raman spectra increase progressively.

Subsurface damage

The SEM micrographs in Fig. 10 show the subsurface damage in the form of microcracks propagated from the surface to the subsurface. These microcracks are formed mainly due to the high brittleness and hardness of the mono-Si, as described by [START_REF] Lawn | Indentation fracture: principles and applications[END_REF]. During penetration of the diamond grains, fragile fracture takes place before plastic deformation occurs, leading to the nucleation and propagation of microcracks into the subsurface of the mono-Si specimen.

According to the subsurface damage analysis reported in Fig. 10, the measured average depth of the microcracks was within the expected range (between 2 and 20 μm from the surface) [START_REF] Möller | Wafer processing[END_REF]. It can be observed that microcracks propagated mainly from the bottom of the grooves of the sawn surface. This is consistent with the restricted orientation of the diamond grains on the wire surface that introduces uniformly aligned microcracks along these periodic grooves. Moreover, many of the microcracks were median microcracks and slightly oblique, as also reported by [START_REF] Xiao | Evaluation of fixed abrasive diamond wire sawing induced subsurface damage of solar silicon wafers[END_REF]. This supports the hypothesis that lateral microcracks propagate to the surface and contribute to fragmented chip formation.

With regard to the cutting parameters, an increase in v f resulted in deeper subsurface microcracks. As seen in Fig. 10a and10b, increasing v f from 20 to 40 mm/min resulted in an increase in the average depth of the microcracks from 9.2 ( ± 1.1) to 11.9 ( ± 0.8) μm. According to [START_REF] Gao | Experiment study on electroplated diamond wire saw slicing single-crystal silicon[END_REF], this increase in the microcrack depth occurs due to the high force per grain, which leads to a greater penetration depth of the kinematic cutting edges and, consequently, higher pressure on the workpiece material. This is in agreement with [START_REF] Klocke | Manufacturing Process 2: Grinding, Honing, Lapping, RWTH[END_REF], who stated that a higher force per grain results in deeper microcracks.

In contrast, when the increase of v c from 10 to 15 m/s (see Fig. 10b and10c), the average depth of the microcracks decreased from 11.9 ( ± 0.8) to 9.6 ( ± 1.0) μm. This reduction may be because an increase in v c leads to a lower h cu value of the diamond grains and reduces the nucleation and propagation of microcracks.

As seen in the Fig. 10d, increasing v c (from 15 to 20 m/s) and decreasing v f (from 40 to 20 mm/min) caused a significant decrease in the subsurface damage, which resulted in an average microcrack depth of 8.1 ( ± 0.9) μm. The microcrack depth analysis showed that for the cutting conditions investigated in this study, lower v f and higher v c results in the lowest microcrack depth. This behavior can be attributed to a smaller undeformed chip thickness (h cu ) and lower force per grain of the diamond grains, leading to less damage to the surface integrity, as verified by the reduction in the microcrack depth.

The average values for the microcrack depth measured under different cutting parameters are shown in Fig. 11. It was found that the microcracks became deeper with an increase in v f , for the same v c and for both wire tensions (T wire ), because this increase allow the h cu,crit for ductile-to-brittle mode transition to be exceeded. This generates deeper microcrack at the subsurface of the mono-Si specimen. The microcracks depth is associated with the morphological characteristics and increases when more craters are present on the sawn surface, exhibited by a high value for the surface roughness. This suggests that the surface morphology is close with subsurface damage. According to the ANOVA results, with a variation in v f from 20 to 40 mm/min the microcrack depth increased by up to 18% (p-value = 0.000169).

On increasing v c and keeping v f constant, for both conditions of T wire , there was a decrease in the microcrack depth. As previously mentioned, the highest v c allows a reduction in the tangential and normal loads of the active diamond grains. Under this condition, there is a lower force per grain, which decreases significantly the initiation and propagation of subsurface microcracks and, consequently, reduces the subsurface damage depth. The ANOVA analysis showed that an increase in v c results in a reduction in the microcrack depth of up to 20% (p-value = 0.000003).

Regarding the cutting parameter T wire, this did not significantly affect the average microcrack depth, as seen in Fig. 11. In the ANOVA analysis, the p-value for the results obtained on increasing T wire from 20 to 30 N was 0.416201, which is higher than α = 0.05. This behavior demonstrates that there is no difference between the average values obtained with a variation in the wire tension (T wire ) under the conditions analyzed in this study.

Conclusions

The cutting of mono-Si using the diamond wire sawing process was experimentally investigated. The experiments were performed applying different cutting parameters in order to evaluate their influence on the surface integrity of the cut mono-Si specimen. Aspects of the brittleductile transition phenomenon were discussed and supported by the surface morphology, surface roughness, identification of the material removal mechanism by residual crystalline phase on the sawn surface and depth of subsurface microcrack damage. Based on the experimental results obtained, it can be concluded that: i. The sawn surface morphology exposed regions which had undergone material removal in the fragile and ductile modes. The predominant mechanism is dependent on the input cutting parameters. An increase in v f led to the formation of more fractures associated with the fragile mode on the sawn surface. An increase in v c favored material removal in the ductile mode, reducing the surface damage. The sawn surfaces analyzed exhibited similar morphology for the two wire tensions (T wire ) tested. ii. An increase in v c resulted in a slight reduction in S a , and increasing v f promoted the higher S a values. This correlation between the v c and v f parameters and the S a value exhibited a similar behavior for both T wire values. For T wire = 30 N, the S a value increased significantly when compared with the specimens sawn using T wire = 20 N. The results for the S a parameter also showed a correlation with the surface morphology observed from the SEM analysis. iii. Raman spectra of the fractured regions exhibited the presence of the Si-I phase, which corresponds to the pure crystal phase of silicon. With a reduction in v f and an increase in v c the sawn surface presented less fractures and more smooth areas with grooves aligned in the wire cutting direction. The grooves exhibited the metastable phases Si-XII and Si-III, as well as the a-Si phase, which indicates that the surface underwent phase transformation due to the grain/ silicon contact pressure. The cutting parameters v c and v f both contributed significantly to the surface formation in the ductile regime, which was evidenced by the presence of the a-Si phase. The variation in T wire had no significant effect on the phase transformation of the sawn surface.

iv. The microcracks in the subsurface originated mainly from the bottom of the machined grooves during the cut. An increase in v f resulted in deeper microcracks, whereas increasing v c resulted in lower microcrack depths. A decrease in v f together with an increase in v c led to lower subsurface microcracks damage. These results

were observed for both wire tensions (T wire ) tested. The T wire no present significate effect on the microcrack depth.

The experimental results for the surface integrity of mono-Si cut using the diamond wire sawing process under different cutting conditions showed that the cutting parameters have a significant influence on the sawn surface quality and the brittle-ductile transition of the mono-Si specimen. In future research the sawing forces could be measured to establish a correlation between the cutting parameters and the formation of subsurface microcracks in the mono-Si specimen.

Fig. 1 .

 1 Fig. 1. Endless wire saw test rig.

Fig. 3 .

 3 Fig. 3. Mono-Si test specimen: (a) dimensions and (b) crystallographic planes in detail.

Fig. 4 .

 4 Fig. 4. Schematic diagram of embedded and bevel-polished specimen.

Fig. 5 .

 5 Fig. 5. SEM micrographs showing the surface morphology of mono-Si specimens sawn under a wire tension of 20 N.

Fig. 6 .

 6 Fig. 6. SEM micrographs showing the surface morphology of mono-Si specimens sawn under a wire tension of 30 N.

Fig. 7 .

 7 Fig. 7. Surface roughness of the mono-Si specimens with variations in the cutting parameters.

Fig. 8 .

 8 Fig. 8. Influence of the wire tension on the kinematic of the cutting process.

Fig. 9 .

 9 Fig. 9. SEM micrographs and respective Raman spectra of sawn surfaces obtained with variations in the cutting parameters.

Fig. 10 .

 10 Fig. 10. SEM micrographs of subsurface of the mono-Si specimens sawn with T wire = 20 N.

Table 1

 1 List of cutting parameters used in the cutting experiments.

	Test	v c (m/s)	v f (mm/min)	T wire (N)
	1	1 0	2 0	2 0
	2	1 0	3 0	2 0
	3	1 0	4 0	2 0
	4	1 5	2 0	2 0
	5	1 5	3 0	2 0
	6	1 5	4 0	2 0
	7	2 0	2 0	2 0
	8	2 0	3 0	2 0
	9	2 0	4 0	2 0
	10	10	20	30
	11	10	30	30
	12	10	40	30
	13	15	20	30
	14	15	30	30
	15	15	40	30
	16	20	20	30
	17	20	30	30
	18	20	40	30

Acknowledgements

The authors would like to thank the Coordination for the Improvement of Higher Education Personnel (CAPES) for the financial support; Saint-Gobain Abrasives for kindly providing the electroplated diamond wires and the Materials Laboratory (LabMat) at UFSC.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.