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Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive
Journal Pre-proof Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive
Jiaohu Huang, Shijin Lu, Fengying Xie, Wei Liu, Caiwei Xiao, Junjie Zhang, Tao Sun PII:
S0264-1275(20)30004-6
DOI:
https://doi.org/10.1016/j.matdes.2020.108471
Reference:
JMADE 108471
To appear in:
Materials & Design
Received date:
7 December 2019
Revised date:
1 January 2020
Accepted date:
2 January 2020
Please cite this article as: J. Huang, S. Lu, F. Xie, et al., Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive, Materials & Design(2020), https://doi.org/10.1016/j.matdes.2020.108471
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© 2020 Published by Elsevier.
Journal Pre-proof
Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive Jiaohu Huang1, Shijin Lu2, Fengying Xie1, Wei Liu1, Caiwei Xiao1,*, Junjie Zhang2,*, Tao Sun2 1
Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621999, China 2
Center for Precision Engineering, Harbin Institute of Technology, Harbin 150001, China Corresponding author: Dr. Caiwei Xiao ([email protected]); Dr. Junjie Zhang
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([email protected])
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Abstract: Synergetic deformation behavior between crystal particles and polymeric binders
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dominates the machinability of energetic materials. In the present work, we elucidate cutting
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mechanisms of HMX-based polymer bonded explosive (PBX) in orthogonal cutting by numerical simulations based on a cohesive finite element framework. The polygonal HMX
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crystals with a particle volume fraction of 90% are modeled by a linear elasticity model, while the HTPB binders are described by a rate-independent hyperelastic model coupled with a
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rate-dependent plasticity model. Furthermore, cohesive elements are implemented in both
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crystal particles and binders to describe thermal-mechanical coupling-induced material failure behavior in the cutting process of PBX. Simulation results reveal different deformation modes of PBX, as well as their correlations with machining results. Furthermore, it is found that depth of cut has a strong impact on the cutting processes of PBX, in terms of material failure mode, subsurface damage and energy dissipation. These findings provide important guidelines for the design and synthesis of energetic materials with high machinability. Key words: Energetic material; synergetic deformation; orthogonal cutting; finite element simulation; cohesive finite element.
1 Introduction Polymer bonded explosive (PBX), which is an important class of commonly used energetic materials, is capable of releasing high amount of chemical energy through redox
Journal Pre-proof reaction under external stimulations [1]. Specifically, mechanical cutting is an important processing and forming method for PBX in engineering fields [2, 3]. In particular, machined surface quality in terms of surface integrity, subsurface damage and surface roughness has a strong impact on the reliability and performance of energetic materials-based devices [4]. For instance, machining-induced flaws greatly deteriorate the safety of energetic materials due to facilitated propensity of hot spot formation [5, 6]. However, achieving high machined surface quality of energetic materials by mechanical cutting is challenging. Specifically, PBX
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possesses poor synergetic deformation behavior between hard crystal particles and soft polymer binders, due to their dramatically different physical and mechanical properties [7].
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Additionally, the complex internal microstructures of PBX in polycrystalline form also induce
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complicated stress and strain phenomenon during machining [8]. Therefore, a thorough
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understanding of fundamental deformation mechanisms of energetic materials under
materials with high machinability.
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mechanical cutting is essentially required to facilitate the design and synthesis of energetic
HMX-based PBX with high energy density is a typical energetic material, which consists
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of HMX crystal particles and polymer binders [9, 10]. In particular, HMX crystal particles in
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PBX have a volume fraction ranging from 60% to 95% [5]. While HMX crystal particles exhibit brittle characteristics, polymer binders such as Estane or HTPB possess high elasticity. Furthermore, the Young's modulus of Estane binders is three to four orders of magnitude lower than that of HMX crystal particles [11, 12]. Therefore, PBX exhibits structural toughness under external loading due to the accommodation of deformation by elastic binder s, thus achieving the mechanical processing of PBX [13]. In order to obtain high machined surface quality of PBX while ensuring the processing safety, it is critical to investigate the deformation behavior in particular damage failure of PBX in mechanical cutting process. The deformation mechanisms of PBX under impact and compression have been investigated experimentally and theoretically. On the experimental side, Palmer et al. [14] carried out compression tests of PBX with real-time microscopic observation, and observed different damage modes of PBX in terms of intra-granular fracture, crystal breakage, binder
Journal Pre-proof fracture, crystal-binder debonding and deformation twins. Zhou et al. [15] found that the fracture of crystal particles is the main failure mode in compression of energetic materials with 95 vol.% HMX crystal particles. Parab et al. [16] reported that the cracking of HMX crystal particles under dynamic compression conditions is mainly caused by the tensile stress generated by contacts between crystal particles. On the theoretical side, finite element (FE) simulations of impact and compression tests have been widely performed to explore microscopic deformation behavior of energetic materials. Austin et al. [17] performed FE
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simulations to investigate the shear region and decomposition reaction of HMX crystal under impact loading, and found that the formation of hot spots is accompanied by the melting of
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shear zone formed at the collapse of the hole. Roy et al. [18] used a cohesive finite element
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(CFE) framework to demonstrate that the ignition tendency of metal-based explosives under
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monotonic impact loading is significantly lower than that of PBX, and the structure integrity is also significantly higher than that of PBX. Grilli et al. [19] employed FE simulations to
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study effects of boundary velocity, initial crack distribution and interface defect on crack propagation and heat generation in dynamic compression of PBX. Keyhani et al. [20] used the
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Lagrangian CFE framework to quantify the ignition probability and dissipation evolution
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caused by plasticity, friction and crack nucleation. They found that specimens with high constituent plasticity or lower internal friction levels are of less sensitivity to ignition. Kim et al. [21] established a CFE framework to analyze the randomness of ignition behavior of PBX by using the probability distribution function. Wei et al. [22] established a FE model of impact of PBX9404 based on a Lagrangian CFE framework, and found that pre-existing defects have a strong influence on the hot spot formation and the ignition threshold. Huang et al. [23, 24] developed a physical model to describe the viscoelastic-plastic deformation, cracking damage, ignition behavior, shock initiation in mild impact of PBX. Although previous work provides valuable insights into the deformation behavior of energetic materials under impact and compression, there is rather limited work reported on the mechanical cutting of energetic materials. Be different from uniform deformation in impact and compression processes with uniaxial stress state, the material undergoes localized
Journal Pre-proof heterogeneous deformation in cutting process with multiaxial stress state. In particular for PBX cutting, it tends to generate high temperature and high pressure in the local contact zone between material and cutting tool, which causes different ignition states of hot spots. On the experimental side, Tang et al. reported three mesoscopic chip shapes of needle, block and scale in turning of PBX, and found that the surface roughness by dry turning is lower than that by wet turning [25, 26]. In addition, they performed ultrasonic vibration-assisted cutting of thin-walled explosives, and found that cutting parameters have a strong impact on the
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correlation of heat generation with cutting temperature [27, 28]. Zhang et al. reported that cutting feed has a more pronounced influence on machined surface finish than cutting speed
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[29]. Xie et al. found that a large depth of cut (DOC) causes edge collapse in milling of
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energetic materials, and the complete edge can be obtained by using a DOC below 0.1 mm [30,
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31]. However, above cutting experiments of energetic materials mainly focus on the characterization of machined surface topography and its dependence on processing
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parameters, and an in-depth understanding of microscopic deformation behavior of energetic materials in cutting process is lacking. On the theoretical side, although FE simulations have
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been widely performed to investigate cutting processes of metals [32-34], polymers [35],
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composites [36-38], semiconductor materials [39, 40] and ceramics [41, 42], there is no FE simulation of mechanical cutting of energetic materials reported. Therefore, in the present work we establish a FE model of orthogonal cutting of HMX-based PBX. A CFE framework is utilized to describe HMX crystal particles and HTPB binders, as well as particle-binder interfaces [43]. Specifically, HMX crystal particles and HTPB binders are set as linear elasticity and rate independent hyperelastic, respectively. In addition, the shape and size of crystal particles are randomly assigned. Subsequently, FE simulations of orthogonal cutting of PBX are performed to investigate the cutting mechanisms of the material, with an emphasis on the microscopic synergetic deformation behavior between different phases and its correlation with marcoscopic machining results. The influence of DOC on the machinability of PBX is further studied.
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2 FE modeling of PBX cutting
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Fig. 1 FE model of orthogonal cutting of PBX.
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Fig. 1 shows the 2D FE model of orthogonal cutting of PBX, which is composed of a
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PBX specimen and a cutting tool. The PBX specimen consists of HMX crystal particles and
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HTPB binders. The specimen has a dimension of 3 mm in length and 1.5 mm in height. In the present work, proportionally-scaled Voronoi polygons are employed to discretize the PBX
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specimen. As show in Fig. 1, the polygon particles are HMX crystals, the gaps between neighboring particles are HTPB binders. The particle-binder interfaces are represented by
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zero thickness cohesive elements. The volume fraction of HMX crystal particles is 90%. While the relationship between size and corresponding volume fraction of crystal particles follows a Gaussian distribution, the average size of crystal particles is 200 μm. The tool modeled as a 2D discrete rigid body has a rake angle and relief angle of 20° and 20°, respectively. In the cutting process, the tool cuts the specimen with a constant DOC and a constant cutting speed of 2 m/s until a cutting distance of 1 mm is reached. To address the influence of DOC, four DOCs of 0.3, 0.4, 0.5 and 0.6 mm are considered. Table 1 lists the utilized cutting parameters in the FE simulations. The rational adoption of constitutive laws to describe crystal particles, binders and crystal particle-binder interfaces in PBX is critical for the prediction accuracy of FE simulations. In the present work, crystal particles and binders are discretized with triangular
Journal Pre-proof elements of 5 μm in size. Furthermore, a Lagrangian CFE framework that inserts cohesive elements at all element boundaries inside the material is used to describe material failure behavior, including random directional
propagation of cracks and debonding of
particle-binder interfaces [44, 45]. This CFE framework eliminates the criteria for crack initiation and propagation, but requires to meet the constraints of mesh density and cohesive stiffness [46]. In addition, this CFE framework also consider the thermal-mechanical coupling process, which is an important aspect for the cutting simulation of energetic materials. The
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triangular constitutive elements and the quadrilateral cohesive elements are co -nodes, and the
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two constitutive elements are connected by one cohesive element, as illustrated in Fig. 2(a).
Cutting speed (m/s) DOC (mm)
Rake angle (°)
Value 2
0.3, 0.4, 0.5, 0.6 0 20 20
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Relief angle (°)
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Edge radius (μm)
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Parameters
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Table 1 Cutting parameters used in FE simulations
Fig. 2 Schematic diagram of CFE framework. (a) The connection method between constitutive element and cohesive element; (b) Bilinear separation criterion for cohesive elements.
There are different kinds of constitutive laws that are used to describe both crystal particles and binders in PBX in previous studies, which are briefly summarized in Table 2.
Journal Pre-proof Giving their brittle characteristics and limited capability of plastic deformation, the relatively rigid HMX crystal particles are modeled by a simpler linear elasticity model [47]. The transition from elastic deformation to ductile delamination, as well as plastic hardening, are important deformation behavior of HTPB binders, which require a synergy between hardening and interfacial degradation inside the binders [48, 49]. Therefore, HTPB binders are described by a coupled model composed of a rate-dependent plasticity model with linear isotropic hardening and a rate-independent hyperelastic model. Table. 3 lists the basic parameters of the
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constitution law for HTPB binders [50, 51]. Furthermore, the bilinear tensile separation criterion shown in Fig. 2(b) is used to describe the deformation behavior of cohesive elements
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[49]. Table. 4 lists a set of parameters used in current PBX configuration [11, 18, 20, 21].
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Table 2 Constitution laws for HMX-based PBX Particle
Explicit/
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Ref.
Matrix
Publication
Material
Constitutuve
Material
Constitutuve
Year
Explicit
HMX
Hyperelastic
Estane
Viscoelastic model
2011
Al
Elasto-viscoplastic
Estane
Viscoelastic model
Estane
Viscoelastic model
2019
Explicit
[20]
Explicit
[21]
Explicit
[22]
Explicit
HMX
HMX
Elasto-viscoplastic
2018
Elasto-viscoplastic
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[18]
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[11]
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Standard
HMX
Elasto-viscoplastic
NC
Viscoelastic model
2018
HMX
Elasto-viscoplastic
NC
Viscoelastic model
2018
Viscoelastic model/
Anisotropic linear [47]
Explicit
Hyperelastic +
HMX
HTPB elasticity
2018 strain-hardening plasticity
[52]
Standard
HMX
Smeared crack model
Estane
Viscoelastic model
2008
Table 3 Parameters of the constitutive law for HTPB binders [47] Material
C10
C01
D1
0y
Hardening Mod.
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0.4MPa
0.45MPa
0.113MPa-1
0.65MPa
0.55MPa
Table 4 Parameters of cohesive elements applied to the PBX [11, 18, 20, 21] Initial separation
Critical tensile stress
Destruction separation
distance (μm)
(MPa)
value (μm)
Crystal particles
0.05
100
5
Matrix
0.01
38.4
10
0.0462
35
4.62
Element position
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Particles – matrix
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interface
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3 Results and discussion
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3.1 Cutting mechanisms of PBX
Fig. 3 FE simulation of orthogonal cutting of PBX with a DOC of 0.4 mm. (a) Variations of cutting force and thrust force with cutting distance; (b) Force analysis in metal cutting; (c) Cutting configuration at a cutting distance of 0.37 mm.
Journal Pre-proof FE simulation of orthogonal cutting of PBX with a DOC of 0.4 mm is firstly performed to explore the involved cutting mechanisms. Fig. 3(a) plots variations of cutting force with cutting distance in the cutting process. It is seen from Fig. 3(a) that cutting force has the same tendency of variations with thrust force, due to the simultaneous contacts of particles with both rake face and clearance face of cutting tool. However, since most of removed material is accumulated in front of cutting tool, cutting force is significantly higher than thrust force. It is seen from Fig. 3(a) that cutting force firstly increases sharply when the tool comes into
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contact with the specimen, and then fluctuates slightly due to debonding of particle-bonder interfaces and fracture of crystal particles. The occurrence of successive crack events in the
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formed chip is accompanied with the sharp decrease of cutting force, which is zero when the
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chip is completely crushed. Fig. 3(a) shows that cutting force remains zero for the cutting
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distance ranging from 0.4 to 0.7 mm, which can be attributed to the air cutting on cavities formed on specimen surface. The observed peaks and valleys in the cutting force-cutting
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distance curve are caused by the time-varying contacts between PBX specimen and rake face
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of cutting tool, accompanied with material accumulation and removal in brittle mode.
Fig. 4 Variation of energy dissipation with cutting distance in the cutting process with a DOC of 0.4 mm.
It is seen from Fig. 3(a) that thrust force around a cutting distance of 0.35 mm is negative, which is different from the case of metal cutting. Fig. 3(b) shows that in metal cutting the material undergoes ductile removal to form continuous chips, and both cutting force and
Journal Pre-proof thrust force are positive. However, Fig. 3(c) demonstrates that there are discontinuous chips formed in the cutting process of PBX, due to the confinement of deformation by internal microstructures, as well as brittle characteristics of HMX crystal particles. The upper part of discontinuous chips slides along rake face of cutting tool, while the lower part is still connected to the specimen and subsequently squeezes the uncut crystal particles. The interaction between crystal particles and cutting tool is localized to single point. Furthermore, the flank face of cutting tool is out of contact with PBX specimen. Therefore, the above two
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aspects jointly leads to the negative value of thrust force. Fig. 4 shows variations of different types of energy dissipation with cutting distance
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during the cutting process with a DOC of 0.4 mm. Specifically, there are four types of energy
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dissipation, as friction dissipation, damage dissipation, plastic dissipation and viscous
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dissipation, respectively. The friction dissipation is caused by the friction between cutting tool and chips. The viscous dissipation is attributed to both body viscous damping and material
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damping. The damage and plastic dissipation is the energy dissipated through damage and plastic deformation, respectively. The friction dissipation and viscous dissipation are the main
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contents of energy dissipation. Specifically, frictional dissipation is the main factor for hot
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spot formation and other dissipations are mainly responsible for global temperature rise, because frictional dissipation is more localized than other dissipations [20, 53]. It is seen from Fig.4 that while the damage dissipation is the lowest, and variations of friction dissipation and viscous dissipation are similar to each other. In addition, Fig. 4 plots variations of external force
work Dis
WE
F
C
with
cutting
distance.
The
external
force
work
is
expressed
as:
FT ds , where Dis is the cutting length, FC is cutting force and FT is thrust
0
force. It is seen from Fig. 4 that both variation characteristics and magnitude of external force work are similar to that of both friction dissipation and viscous dissipation. In the highly localized contact zone between cutting tool and material, the large amount of removed material is accumulated in front of cutting tool, so the energy dissipation by friction and viscous between removed material and rake face of cutting tool is dominant over the other
Journal Pre-proof two types of energy dissipation. Therefore, external force work can be used as an approximate
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indicator for representing hot spot formation and temperature change.
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Fig. 5 Cutting configurations in cutting process with a DOC of 0.4 mm. Cutting distance: (a) 0.064 mm; (b) 0.338mm; (c) 0.420mm; (d) 1.000mm.
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Fig. 5 shows representative cutting configurations under the DOC of 0.4 mm at different cutting distances, which are also marked with black lines in Fig. 3(a). Fig. 5(a) shows that the
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initial contact between cutting tool and specimen leads to a significant stress concentration in front of cutting edge, which leads to internal broken of the contacted particle. Furthermore, there is also stress concentration propagated into neighboring particles observed. Fig. 5(b) presents that the expansion of stress concentration region finally leads to successive fracture s of neighboring crystal particles, accompanied with block removal of crystal particles and binders. Figs. 5(c) and (d) show that a single chip block may contain one or more crystal particles. Fig. 5 also highlights different deformation modes of crystal particles with red ellipses. Specifically, the ellipse 1, 2, 3 and 4 indicates fracture, pull out, squeeze out and push out of crystal particles, respectively. In addition to deformation and failure of crystal particles, there is significant deformation of HTTP binders observed. Specifically, there are binder filaments that bridge the
Journal Pre-proof crack walls formed, which is also experimentally observed by Rae et al. [13]. In the cutting process, the binders between crystal particles are firstly stretched by crystal particle-tool edge interactions, as well as deformation of connecting crystal particles, as shown in Fig. 5(b). With the advance of tool edge, two types of binder deformation are observed, as marked by green rectangular in Fig. 5. Specifically, position 5 in Fig. 5(c) indicates that the binder is still unbroken after the broken of conterminal particles, and will recover to its original shape. Consequently, the fragments of partially broken crystal particles will remain in the specimen
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due to the elastic behavior of the binders. In contrast, Fig. 5(d) shows that the binder at position 6 is stretched to be broken, and then is removed together with conterminal crystal
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particles. Fig. 5 also indicates stretching and broken of binders under cutting path, which
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directly deteriorate machined surface quality.
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Figs. 6(a) to (h) present cutting configurations of the first (left column) and the last (right column) crystal particle on the cutting path. Furthermore, the position of the first and the last
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particle is marked with a red triangle and a five-pointed star in Fig. 1, respectively. The crystal particle-tool edge interaction leads to stress concentration formed, which subsequently
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leads to initiation of a random crack. The formed crack then propagates until it penetrates
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through the whole crystal particle, which results into splitting of the crystal particle splits into two parts. However, the crack propagation direction is divided into lateral and longitudinal expansion for the first crystal particle and the other crystal particles, respectively. It is seen from Fig. 6 that the laterally expanded crack finally leads to formation of high surface integrity, while the longitudinally expanded crack eventually results into cavity formation. While crystal particles on the cutting path are partially broken, there is no broken of binders on the cutting path observed.
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Fig. 6 Cutting configurations of the first crystal particle at a cutting distance of (a) 0.068 mm, (c) 0.080 mm, (e) 0.120 mm and (g) 0.166 mm; Cutting configurations of the last crystal particle at a cutting distance of (b) 0.720 mm, (d) 0.740 mm, (f) 0.760 mm and (h) 0.800 mm.
3.2 Influence of DOC In addition to the DOC of 0.4 mm, FE simulations of PBX cutting using other three
Journal Pre-proof DOCs of 0.3 mm, 0.5 mm and 0.6 mm are also performed to address the influence of DOC. Fig. 7 presents cutting configurations of PBX specimen at the same cutting distance of 1 mm for the four DOCs. For each DOC, the crystal particle adjacent to the cutting edge is broken. The above mentioned four typical failure modes of crystal particles, i.e. fracture, pull out,
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squeeze out and push out, are also found for each DOC.
Fig. 7 Cutting configurations of PBX at a cutting distance of 1 mm for a DOC of (a) 0.3 mm; (b) 0.4 mm;
Journal Pre-proof (c) 0.5 mm; (d) 0.6 mm.
However, Fig. 7 demonstrates that the DOC has a strong influence on deformation behavior of PBX under cutting process. For the DOC of 0.3 mm, crystal particles on the cutting path are removed through fracture. With the increase of DOC, machined surface integrity decreases, accompanied with the increase of subsurface damage due to increased amount of debonding of crystal particle-binder interfaces. In addition, chip formation varies significantly for different DOCs. For the DOC of 0.3 or 0.4 mm, the chips are mainly
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composed of limited individual crystal particles dislodged from the specimen. In contrast, for
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the DOC of 0.5 or 0.6 mm, the chips at the edge of the specimen are composed of unbroken blocks that contain lager numbers of crystal particles. Furthermore, crystal particles begin to
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dislodge one by one from the PBX specimen under the cutting action for large DOCs. Fig. 7
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demonstrates that the best machined surface integrity can be obtained for the DOC of 0.4 mm.
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While interactions of crystal particles and binders with cutting tool are strongly affected by the relative positions of crystal particles and binders with cutting path, Fig. 7 also indicates
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two new deformation modes of PBX in cutting that are not observed in the cutting process with a DOC of 0.4 mm. Specifically, Fig. 7(a) indicates that the surface layer of the crystal
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particle highlighted by position 1 is broken by squeezing action. However, Fig. 7(d) shows that the crystal particles indicated by position 2 are slipped relatively to surrounding particles. Fig. 8(a) and (b) plots the variation of cutting force and thrust force for the four DOCs, respectively. The cutting force and thrust force for the DOC of 0.5 or 0.6 mm at a cutting distance between 0 and 0.32 mm is significant higher than that for the DOC of 0.3 or 0.4 mm. In particular for the cutting distance ranging from 0.53 to 1.0 mm, the values of cutting force and thrust force for the DOC of 0.5 or 0.6 mm are zero, while the force values for the DOC of 0.3 mm or 0.4 mm fluctuate around constant values. Fig. 9(a), (b), (c) and (d) plots variations of damage dissipation, frictional dissipation, plastic dissipation and viscous dissipation with cutting distance for the four DOCs, respectively. Fig. 9 indicates that friction dissipation and viscous dissipation are the main
Journal Pre-proof components of energy dissipation for each DOC. In particular for the low DOCs of 0.3 and 0.4 mm, the variation characteristics of friction dissipation, viscous dissipation and plastic dissipation are similar to each other. However, both friction dissipation, viscous dissipation and plastic dissipation increase dramatically for the high DOCs of 0.5 and 0.6 mm. The is no monotonous dependence of damage dissipation on the DOC observed, due to irregular relative positions of tool edge with internal microstructures of PBX. Friction dissipation and viscous dissipation correspond to the variation of cutting force. When the cutting force is zero, i.e., air
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cutting on cavity, the energy dissipation maintains a fixed value. Therefore, it indicates that friction dissipation and viscous dissipation are mainly caused by tool-material interaction.
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The variation magnitude of plastic dissipation is different from that of friction dissipation and
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viscous dissipation, which indicates that plastic dissipation is also caused by plastic
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deformation of binders. By comparing the variation characteristics of energy dissipation with
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damage dissipation.
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material damage shown in Fig. 7, it can be reached that particle fracture dominates the
Fig. 8 Variations of (a) cutting force and (b) thrust force with cutting distance in cutting processes with four different DOCs.
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Fig. 9 Energy dissipation in PBX cutting with four DOCs. (a) Damage dissipation; (b) Frictional
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4 Conclusions
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dissipation; (c) Plastic dissipation; (d) Viscous dissipation.
In summary, we performed 2D FE simulations to elucidate cutting mechanisms involved
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in orthogonal cutting of HMX-based PBX. Based on a CFE framework, the material failure
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behavior including fracture of both crystal particles and binders, as well as debonding of particle-binder interfaces, were described by the implementation of cohesive elements. The HMX crystal particles shaped with proportionally-scaled Voronoi polygons has a particle volume fraction of 90%, and were modeled by a linear elasticity model. The HTPB binders were described by a rate-independent hyperelastic model coupled with a rate-dependent plasticity model. Simulation results revealed different interactions of crystal particles with tool edge, including fracture, pull out, squeeze out and push out of HMX crystal particles. While the laterally propagated crack finally led to formation of machined surface with high surface integrity, the longitudinally expanded crack eventually resulted into cavity formation. In particular for crystal particles residing on the cutting path, the failure mode s of crystal particles were closely associated with binder deformation. While friction dissipation and viscous dissipation were the main components of energy dissipation, the variation trend and
Journal Pre-proof size of external work were similar to friction loss and viscous loss. It was found that DOC has a strong impact on deformation behavior of PBX and correlated machining results. While cutting force increased with increasing DOC, a critical DOC of 0.4 mm for the best machined surface quality was found.
Acknowledgement The authors greatly acknowledge supports from the National Natural Science Foundation
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of China (grant number 51505441) and the Fundamental Research Funds for the Central
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Universities.
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Data Availability
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The raw/processed data required to reproduce these findings cannot be shared at this time
Reference
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as the data also forms part of an ongoing study.
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[42] J.J. Zhang, L. Han, J.G. Zhang, H.Y. Liu, Y.D. Yan, T. Sun. Brittle-to-ductile transition in elliptical vibration-assisted diamond cutting of reaction-bonded silicon carbide. Journal of Manufacturing Processes, 2019, 45: 670-681. [43] H.D. Espinosa, P.D. Zavattieri, S.K. Dwivedi. A finite deformation continuum: Discrete model for the description of fragmentation and damage in brittle materials. Journal of The Mechanics And Physics Of Solids, 1998, 46 (10): 1909-1942. [44] J. Zhai, M. Zhou. Finite element analysis of micromechanical failure modes in a heterogeneous ceramic material system. International Journal of Fracture, 2000, 101 (1 -2): 161-180.
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Cohesive Finite Element Method. Journal of Engineering Materials and Technology, 2004,
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Experimentally-validated mesoscale modeling of the coupled mechanical–thermal response of AP–HTPB energetic material under dynamic loading. International Journal of Fracture, 2017, 203 (1-2): 277-298.
[51] J.S. Xu, X. Chen, H.L. Wang, J. Zheng, C.S. Zhou. Thermo-damage-viscoelastic constitutive model of HTPB composite propellant. International Journal of Solids and Structures, 2014, 51 (18): 3209-3217. [52] Y.Q. Wu, F.L. Huang. A micromechanical model for predicting combined damage of particles and interface debonding in PBX explosives. Mechanics of Materials, 2009, 41 (1): 27-47. [53] R. Liu, P.W. Chen. Modeling ignition prediction of HMX-based polymer bonded explosives under low velocity impact. Mechanics of Materials, 2018, 124: 106 -117.
Journal Pre-proof Credit Author Statement Jiaohu Huang: Conceptualization, Methodology, Supervision, Writing-Review & Editing; Shijin Lu: Software, Formal analysis, Visualization, Writing-Original Draft; Fengying Xie: Methodology, validation, Investigation, Writing-Original Draft; Wei Liu: Conceptualization,
Supervision;
Caiwei
Xiao:
Conceptualization,
Methodology,
Writing-Review & Editing, Project administration; Junjie Zhang: Conceptualization,
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Supervision, Resources, Writing-Review & Editing; Tao Sun: Supervision.
Journal Pre-proof Declaration of interests The authors declare that they have no known competing financial interests or personal
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relationships that could have appeared to influence the work reported in this paper.
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Graphical abstract
Journal Pre-proof Highlights Synergetic cutting mechanisms of PBX energetic material were revealed by cohesive finite element simulations for the first time. Cohesive elements were implemented to describe fracture of both crystal particles and binders, as well as debonding of particle-binder interface in PBX cutting. Crystal particles failure modes of fracture, pull out, squeeze out and push out, and their
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correlations with machined surface topography, were revealed.
Jiaohu Huang, Shijin Lu, Fengying Xie, Wei Liu, Caiwei Xiao, Junjie Zhang, Tao Sun PII:
S0264-1275(20)30004-6
DOI:
https://doi.org/10.1016/j.matdes.2020.108471
Reference:
JMADE 108471
To appear in:
Materials & Design
Received date:
7 December 2019
Revised date:
1 January 2020
Accepted date:
2 January 2020
Please cite this article as: J. Huang, S. Lu, F. Xie, et al., Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive, Materials & Design(2020), https://doi.org/10.1016/j.matdes.2020.108471
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© 2020 Published by Elsevier.
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Finite element analysis of synergetic deformation in precision cutting of polymer bonded explosive Jiaohu Huang1, Shijin Lu2, Fengying Xie1, Wei Liu1, Caiwei Xiao1,*, Junjie Zhang2,*, Tao Sun2 1
Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621999, China 2
Center for Precision Engineering, Harbin Institute of Technology, Harbin 150001, China Corresponding author: Dr. Caiwei Xiao ([email protected]); Dr. Junjie Zhang
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([email protected])
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Abstract: Synergetic deformation behavior between crystal particles and polymeric binders
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dominates the machinability of energetic materials. In the present work, we elucidate cutting
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mechanisms of HMX-based polymer bonded explosive (PBX) in orthogonal cutting by numerical simulations based on a cohesive finite element framework. The polygonal HMX
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crystals with a particle volume fraction of 90% are modeled by a linear elasticity model, while the HTPB binders are described by a rate-independent hyperelastic model coupled with a
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rate-dependent plasticity model. Furthermore, cohesive elements are implemented in both
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crystal particles and binders to describe thermal-mechanical coupling-induced material failure behavior in the cutting process of PBX. Simulation results reveal different deformation modes of PBX, as well as their correlations with machining results. Furthermore, it is found that depth of cut has a strong impact on the cutting processes of PBX, in terms of material failure mode, subsurface damage and energy dissipation. These findings provide important guidelines for the design and synthesis of energetic materials with high machinability. Key words: Energetic material; synergetic deformation; orthogonal cutting; finite element simulation; cohesive finite element.
1 Introduction Polymer bonded explosive (PBX), which is an important class of commonly used energetic materials, is capable of releasing high amount of chemical energy through redox
Journal Pre-proof reaction under external stimulations [1]. Specifically, mechanical cutting is an important processing and forming method for PBX in engineering fields [2, 3]. In particular, machined surface quality in terms of surface integrity, subsurface damage and surface roughness has a strong impact on the reliability and performance of energetic materials-based devices [4]. For instance, machining-induced flaws greatly deteriorate the safety of energetic materials due to facilitated propensity of hot spot formation [5, 6]. However, achieving high machined surface quality of energetic materials by mechanical cutting is challenging. Specifically, PBX
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possesses poor synergetic deformation behavior between hard crystal particles and soft polymer binders, due to their dramatically different physical and mechanical properties [7].
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Additionally, the complex internal microstructures of PBX in polycrystalline form also induce
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complicated stress and strain phenomenon during machining [8]. Therefore, a thorough
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understanding of fundamental deformation mechanisms of energetic materials under
materials with high machinability.
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mechanical cutting is essentially required to facilitate the design and synthesis of energetic
HMX-based PBX with high energy density is a typical energetic material, which consists
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of HMX crystal particles and polymer binders [9, 10]. In particular, HMX crystal particles in
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PBX have a volume fraction ranging from 60% to 95% [5]. While HMX crystal particles exhibit brittle characteristics, polymer binders such as Estane or HTPB possess high elasticity. Furthermore, the Young's modulus of Estane binders is three to four orders of magnitude lower than that of HMX crystal particles [11, 12]. Therefore, PBX exhibits structural toughness under external loading due to the accommodation of deformation by elastic binder s, thus achieving the mechanical processing of PBX [13]. In order to obtain high machined surface quality of PBX while ensuring the processing safety, it is critical to investigate the deformation behavior in particular damage failure of PBX in mechanical cutting process. The deformation mechanisms of PBX under impact and compression have been investigated experimentally and theoretically. On the experimental side, Palmer et al. [14] carried out compression tests of PBX with real-time microscopic observation, and observed different damage modes of PBX in terms of intra-granular fracture, crystal breakage, binder
Journal Pre-proof fracture, crystal-binder debonding and deformation twins. Zhou et al. [15] found that the fracture of crystal particles is the main failure mode in compression of energetic materials with 95 vol.% HMX crystal particles. Parab et al. [16] reported that the cracking of HMX crystal particles under dynamic compression conditions is mainly caused by the tensile stress generated by contacts between crystal particles. On the theoretical side, finite element (FE) simulations of impact and compression tests have been widely performed to explore microscopic deformation behavior of energetic materials. Austin et al. [17] performed FE
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simulations to investigate the shear region and decomposition reaction of HMX crystal under impact loading, and found that the formation of hot spots is accompanied by the melting of
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shear zone formed at the collapse of the hole. Roy et al. [18] used a cohesive finite element
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(CFE) framework to demonstrate that the ignition tendency of metal-based explosives under
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monotonic impact loading is significantly lower than that of PBX, and the structure integrity is also significantly higher than that of PBX. Grilli et al. [19] employed FE simulations to
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study effects of boundary velocity, initial crack distribution and interface defect on crack propagation and heat generation in dynamic compression of PBX. Keyhani et al. [20] used the
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Lagrangian CFE framework to quantify the ignition probability and dissipation evolution
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caused by plasticity, friction and crack nucleation. They found that specimens with high constituent plasticity or lower internal friction levels are of less sensitivity to ignition. Kim et al. [21] established a CFE framework to analyze the randomness of ignition behavior of PBX by using the probability distribution function. Wei et al. [22] established a FE model of impact of PBX9404 based on a Lagrangian CFE framework, and found that pre-existing defects have a strong influence on the hot spot formation and the ignition threshold. Huang et al. [23, 24] developed a physical model to describe the viscoelastic-plastic deformation, cracking damage, ignition behavior, shock initiation in mild impact of PBX. Although previous work provides valuable insights into the deformation behavior of energetic materials under impact and compression, there is rather limited work reported on the mechanical cutting of energetic materials. Be different from uniform deformation in impact and compression processes with uniaxial stress state, the material undergoes localized
Journal Pre-proof heterogeneous deformation in cutting process with multiaxial stress state. In particular for PBX cutting, it tends to generate high temperature and high pressure in the local contact zone between material and cutting tool, which causes different ignition states of hot spots. On the experimental side, Tang et al. reported three mesoscopic chip shapes of needle, block and scale in turning of PBX, and found that the surface roughness by dry turning is lower than that by wet turning [25, 26]. In addition, they performed ultrasonic vibration-assisted cutting of thin-walled explosives, and found that cutting parameters have a strong impact on the
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correlation of heat generation with cutting temperature [27, 28]. Zhang et al. reported that cutting feed has a more pronounced influence on machined surface finish than cutting speed
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[29]. Xie et al. found that a large depth of cut (DOC) causes edge collapse in milling of
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energetic materials, and the complete edge can be obtained by using a DOC below 0.1 mm [30,
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31]. However, above cutting experiments of energetic materials mainly focus on the characterization of machined surface topography and its dependence on processing
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parameters, and an in-depth understanding of microscopic deformation behavior of energetic materials in cutting process is lacking. On the theoretical side, although FE simulations have
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been widely performed to investigate cutting processes of metals [32-34], polymers [35],
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composites [36-38], semiconductor materials [39, 40] and ceramics [41, 42], there is no FE simulation of mechanical cutting of energetic materials reported. Therefore, in the present work we establish a FE model of orthogonal cutting of HMX-based PBX. A CFE framework is utilized to describe HMX crystal particles and HTPB binders, as well as particle-binder interfaces [43]. Specifically, HMX crystal particles and HTPB binders are set as linear elasticity and rate independent hyperelastic, respectively. In addition, the shape and size of crystal particles are randomly assigned. Subsequently, FE simulations of orthogonal cutting of PBX are performed to investigate the cutting mechanisms of the material, with an emphasis on the microscopic synergetic deformation behavior between different phases and its correlation with marcoscopic machining results. The influence of DOC on the machinability of PBX is further studied.
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2 FE modeling of PBX cutting
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Fig. 1 FE model of orthogonal cutting of PBX.
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Fig. 1 shows the 2D FE model of orthogonal cutting of PBX, which is composed of a
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PBX specimen and a cutting tool. The PBX specimen consists of HMX crystal particles and
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HTPB binders. The specimen has a dimension of 3 mm in length and 1.5 mm in height. In the present work, proportionally-scaled Voronoi polygons are employed to discretize the PBX
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specimen. As show in Fig. 1, the polygon particles are HMX crystals, the gaps between neighboring particles are HTPB binders. The particle-binder interfaces are represented by
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zero thickness cohesive elements. The volume fraction of HMX crystal particles is 90%. While the relationship between size and corresponding volume fraction of crystal particles follows a Gaussian distribution, the average size of crystal particles is 200 μm. The tool modeled as a 2D discrete rigid body has a rake angle and relief angle of 20° and 20°, respectively. In the cutting process, the tool cuts the specimen with a constant DOC and a constant cutting speed of 2 m/s until a cutting distance of 1 mm is reached. To address the influence of DOC, four DOCs of 0.3, 0.4, 0.5 and 0.6 mm are considered. Table 1 lists the utilized cutting parameters in the FE simulations. The rational adoption of constitutive laws to describe crystal particles, binders and crystal particle-binder interfaces in PBX is critical for the prediction accuracy of FE simulations. In the present work, crystal particles and binders are discretized with triangular
Journal Pre-proof elements of 5 μm in size. Furthermore, a Lagrangian CFE framework that inserts cohesive elements at all element boundaries inside the material is used to describe material failure behavior, including random directional
propagation of cracks and debonding of
particle-binder interfaces [44, 45]. This CFE framework eliminates the criteria for crack initiation and propagation, but requires to meet the constraints of mesh density and cohesive stiffness [46]. In addition, this CFE framework also consider the thermal-mechanical coupling process, which is an important aspect for the cutting simulation of energetic materials. The
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triangular constitutive elements and the quadrilateral cohesive elements are co -nodes, and the
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two constitutive elements are connected by one cohesive element, as illustrated in Fig. 2(a).
Cutting speed (m/s) DOC (mm)
Rake angle (°)
Value 2
0.3, 0.4, 0.5, 0.6 0 20 20
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Relief angle (°)
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Edge radius (μm)
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Parameters
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Table 1 Cutting parameters used in FE simulations
Fig. 2 Schematic diagram of CFE framework. (a) The connection method between constitutive element and cohesive element; (b) Bilinear separation criterion for cohesive elements.
There are different kinds of constitutive laws that are used to describe both crystal particles and binders in PBX in previous studies, which are briefly summarized in Table 2.
Journal Pre-proof Giving their brittle characteristics and limited capability of plastic deformation, the relatively rigid HMX crystal particles are modeled by a simpler linear elasticity model [47]. The transition from elastic deformation to ductile delamination, as well as plastic hardening, are important deformation behavior of HTPB binders, which require a synergy between hardening and interfacial degradation inside the binders [48, 49]. Therefore, HTPB binders are described by a coupled model composed of a rate-dependent plasticity model with linear isotropic hardening and a rate-independent hyperelastic model. Table. 3 lists the basic parameters of the
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constitution law for HTPB binders [50, 51]. Furthermore, the bilinear tensile separation criterion shown in Fig. 2(b) is used to describe the deformation behavior of cohesive elements
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[49]. Table. 4 lists a set of parameters used in current PBX configuration [11, 18, 20, 21].
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Table 2 Constitution laws for HMX-based PBX Particle
Explicit/
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Ref.
Matrix
Publication
Material
Constitutuve
Material
Constitutuve
Year
Explicit
HMX
Hyperelastic
Estane
Viscoelastic model
2011
Al
Elasto-viscoplastic
Estane
Viscoelastic model
Estane
Viscoelastic model
2019
Explicit
[20]
Explicit
[21]
Explicit
[22]
Explicit
HMX
HMX
Elasto-viscoplastic
2018
Elasto-viscoplastic
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[18]
na
[11]
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Standard
HMX
Elasto-viscoplastic
NC
Viscoelastic model
2018
HMX
Elasto-viscoplastic
NC
Viscoelastic model
2018
Viscoelastic model/
Anisotropic linear [47]
Explicit
Hyperelastic +
HMX
HTPB elasticity
2018 strain-hardening plasticity
[52]
Standard
HMX
Smeared crack model
Estane
Viscoelastic model
2008
Table 3 Parameters of the constitutive law for HTPB binders [47] Material
C10
C01
D1
0y
Hardening Mod.
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0.4MPa
0.45MPa
0.113MPa-1
0.65MPa
0.55MPa
Table 4 Parameters of cohesive elements applied to the PBX [11, 18, 20, 21] Initial separation
Critical tensile stress
Destruction separation
distance (μm)
(MPa)
value (μm)
Crystal particles
0.05
100
5
Matrix
0.01
38.4
10
0.0462
35
4.62
Element position
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Particles – matrix
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interface
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3 Results and discussion
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3.1 Cutting mechanisms of PBX
Fig. 3 FE simulation of orthogonal cutting of PBX with a DOC of 0.4 mm. (a) Variations of cutting force and thrust force with cutting distance; (b) Force analysis in metal cutting; (c) Cutting configuration at a cutting distance of 0.37 mm.
Journal Pre-proof FE simulation of orthogonal cutting of PBX with a DOC of 0.4 mm is firstly performed to explore the involved cutting mechanisms. Fig. 3(a) plots variations of cutting force with cutting distance in the cutting process. It is seen from Fig. 3(a) that cutting force has the same tendency of variations with thrust force, due to the simultaneous contacts of particles with both rake face and clearance face of cutting tool. However, since most of removed material is accumulated in front of cutting tool, cutting force is significantly higher than thrust force. It is seen from Fig. 3(a) that cutting force firstly increases sharply when the tool comes into
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contact with the specimen, and then fluctuates slightly due to debonding of particle-bonder interfaces and fracture of crystal particles. The occurrence of successive crack events in the
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formed chip is accompanied with the sharp decrease of cutting force, which is zero when the
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chip is completely crushed. Fig. 3(a) shows that cutting force remains zero for the cutting
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distance ranging from 0.4 to 0.7 mm, which can be attributed to the air cutting on cavities formed on specimen surface. The observed peaks and valleys in the cutting force-cutting
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distance curve are caused by the time-varying contacts between PBX specimen and rake face
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of cutting tool, accompanied with material accumulation and removal in brittle mode.
Fig. 4 Variation of energy dissipation with cutting distance in the cutting process with a DOC of 0.4 mm.
It is seen from Fig. 3(a) that thrust force around a cutting distance of 0.35 mm is negative, which is different from the case of metal cutting. Fig. 3(b) shows that in metal cutting the material undergoes ductile removal to form continuous chips, and both cutting force and
Journal Pre-proof thrust force are positive. However, Fig. 3(c) demonstrates that there are discontinuous chips formed in the cutting process of PBX, due to the confinement of deformation by internal microstructures, as well as brittle characteristics of HMX crystal particles. The upper part of discontinuous chips slides along rake face of cutting tool, while the lower part is still connected to the specimen and subsequently squeezes the uncut crystal particles. The interaction between crystal particles and cutting tool is localized to single point. Furthermore, the flank face of cutting tool is out of contact with PBX specimen. Therefore, the above two
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aspects jointly leads to the negative value of thrust force. Fig. 4 shows variations of different types of energy dissipation with cutting distance
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during the cutting process with a DOC of 0.4 mm. Specifically, there are four types of energy
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dissipation, as friction dissipation, damage dissipation, plastic dissipation and viscous
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dissipation, respectively. The friction dissipation is caused by the friction between cutting tool and chips. The viscous dissipation is attributed to both body viscous damping and material
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damping. The damage and plastic dissipation is the energy dissipated through damage and plastic deformation, respectively. The friction dissipation and viscous dissipation are the main
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contents of energy dissipation. Specifically, frictional dissipation is the main factor for hot
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spot formation and other dissipations are mainly responsible for global temperature rise, because frictional dissipation is more localized than other dissipations [20, 53]. It is seen from Fig.4 that while the damage dissipation is the lowest, and variations of friction dissipation and viscous dissipation are similar to each other. In addition, Fig. 4 plots variations of external force
work Dis
WE
F
C
with
cutting
distance.
The
external
force
work
is
expressed
as:
FT ds , where Dis is the cutting length, FC is cutting force and FT is thrust
0
force. It is seen from Fig. 4 that both variation characteristics and magnitude of external force work are similar to that of both friction dissipation and viscous dissipation. In the highly localized contact zone between cutting tool and material, the large amount of removed material is accumulated in front of cutting tool, so the energy dissipation by friction and viscous between removed material and rake face of cutting tool is dominant over the other
Journal Pre-proof two types of energy dissipation. Therefore, external force work can be used as an approximate
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indicator for representing hot spot formation and temperature change.
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Fig. 5 Cutting configurations in cutting process with a DOC of 0.4 mm. Cutting distance: (a) 0.064 mm; (b) 0.338mm; (c) 0.420mm; (d) 1.000mm.
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Fig. 5 shows representative cutting configurations under the DOC of 0.4 mm at different cutting distances, which are also marked with black lines in Fig. 3(a). Fig. 5(a) shows that the
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initial contact between cutting tool and specimen leads to a significant stress concentration in front of cutting edge, which leads to internal broken of the contacted particle. Furthermore, there is also stress concentration propagated into neighboring particles observed. Fig. 5(b) presents that the expansion of stress concentration region finally leads to successive fracture s of neighboring crystal particles, accompanied with block removal of crystal particles and binders. Figs. 5(c) and (d) show that a single chip block may contain one or more crystal particles. Fig. 5 also highlights different deformation modes of crystal particles with red ellipses. Specifically, the ellipse 1, 2, 3 and 4 indicates fracture, pull out, squeeze out and push out of crystal particles, respectively. In addition to deformation and failure of crystal particles, there is significant deformation of HTTP binders observed. Specifically, there are binder filaments that bridge the
Journal Pre-proof crack walls formed, which is also experimentally observed by Rae et al. [13]. In the cutting process, the binders between crystal particles are firstly stretched by crystal particle-tool edge interactions, as well as deformation of connecting crystal particles, as shown in Fig. 5(b). With the advance of tool edge, two types of binder deformation are observed, as marked by green rectangular in Fig. 5. Specifically, position 5 in Fig. 5(c) indicates that the binder is still unbroken after the broken of conterminal particles, and will recover to its original shape. Consequently, the fragments of partially broken crystal particles will remain in the specimen
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due to the elastic behavior of the binders. In contrast, Fig. 5(d) shows that the binder at position 6 is stretched to be broken, and then is removed together with conterminal crystal
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particles. Fig. 5 also indicates stretching and broken of binders under cutting path, which
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directly deteriorate machined surface quality.
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Figs. 6(a) to (h) present cutting configurations of the first (left column) and the last (right column) crystal particle on the cutting path. Furthermore, the position of the first and the last
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particle is marked with a red triangle and a five-pointed star in Fig. 1, respectively. The crystal particle-tool edge interaction leads to stress concentration formed, which subsequently
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leads to initiation of a random crack. The formed crack then propagates until it penetrates
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through the whole crystal particle, which results into splitting of the crystal particle splits into two parts. However, the crack propagation direction is divided into lateral and longitudinal expansion for the first crystal particle and the other crystal particles, respectively. It is seen from Fig. 6 that the laterally expanded crack finally leads to formation of high surface integrity, while the longitudinally expanded crack eventually results into cavity formation. While crystal particles on the cutting path are partially broken, there is no broken of binders on the cutting path observed.
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Fig. 6 Cutting configurations of the first crystal particle at a cutting distance of (a) 0.068 mm, (c) 0.080 mm, (e) 0.120 mm and (g) 0.166 mm; Cutting configurations of the last crystal particle at a cutting distance of (b) 0.720 mm, (d) 0.740 mm, (f) 0.760 mm and (h) 0.800 mm.
3.2 Influence of DOC In addition to the DOC of 0.4 mm, FE simulations of PBX cutting using other three
Journal Pre-proof DOCs of 0.3 mm, 0.5 mm and 0.6 mm are also performed to address the influence of DOC. Fig. 7 presents cutting configurations of PBX specimen at the same cutting distance of 1 mm for the four DOCs. For each DOC, the crystal particle adjacent to the cutting edge is broken. The above mentioned four typical failure modes of crystal particles, i.e. fracture, pull out,
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squeeze out and push out, are also found for each DOC.
Fig. 7 Cutting configurations of PBX at a cutting distance of 1 mm for a DOC of (a) 0.3 mm; (b) 0.4 mm;
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However, Fig. 7 demonstrates that the DOC has a strong influence on deformation behavior of PBX under cutting process. For the DOC of 0.3 mm, crystal particles on the cutting path are removed through fracture. With the increase of DOC, machined surface integrity decreases, accompanied with the increase of subsurface damage due to increased amount of debonding of crystal particle-binder interfaces. In addition, chip formation varies significantly for different DOCs. For the DOC of 0.3 or 0.4 mm, the chips are mainly
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composed of limited individual crystal particles dislodged from the specimen. In contrast, for
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the DOC of 0.5 or 0.6 mm, the chips at the edge of the specimen are composed of unbroken blocks that contain lager numbers of crystal particles. Furthermore, crystal particles begin to
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dislodge one by one from the PBX specimen under the cutting action for large DOCs. Fig. 7
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demonstrates that the best machined surface integrity can be obtained for the DOC of 0.4 mm.
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While interactions of crystal particles and binders with cutting tool are strongly affected by the relative positions of crystal particles and binders with cutting path, Fig. 7 also indicates
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two new deformation modes of PBX in cutting that are not observed in the cutting process with a DOC of 0.4 mm. Specifically, Fig. 7(a) indicates that the surface layer of the crystal
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particle highlighted by position 1 is broken by squeezing action. However, Fig. 7(d) shows that the crystal particles indicated by position 2 are slipped relatively to surrounding particles. Fig. 8(a) and (b) plots the variation of cutting force and thrust force for the four DOCs, respectively. The cutting force and thrust force for the DOC of 0.5 or 0.6 mm at a cutting distance between 0 and 0.32 mm is significant higher than that for the DOC of 0.3 or 0.4 mm. In particular for the cutting distance ranging from 0.53 to 1.0 mm, the values of cutting force and thrust force for the DOC of 0.5 or 0.6 mm are zero, while the force values for the DOC of 0.3 mm or 0.4 mm fluctuate around constant values. Fig. 9(a), (b), (c) and (d) plots variations of damage dissipation, frictional dissipation, plastic dissipation and viscous dissipation with cutting distance for the four DOCs, respectively. Fig. 9 indicates that friction dissipation and viscous dissipation are the main
Journal Pre-proof components of energy dissipation for each DOC. In particular for the low DOCs of 0.3 and 0.4 mm, the variation characteristics of friction dissipation, viscous dissipation and plastic dissipation are similar to each other. However, both friction dissipation, viscous dissipation and plastic dissipation increase dramatically for the high DOCs of 0.5 and 0.6 mm. The is no monotonous dependence of damage dissipation on the DOC observed, due to irregular relative positions of tool edge with internal microstructures of PBX. Friction dissipation and viscous dissipation correspond to the variation of cutting force. When the cutting force is zero, i.e., air
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cutting on cavity, the energy dissipation maintains a fixed value. Therefore, it indicates that friction dissipation and viscous dissipation are mainly caused by tool-material interaction.
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The variation magnitude of plastic dissipation is different from that of friction dissipation and
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viscous dissipation, which indicates that plastic dissipation is also caused by plastic
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deformation of binders. By comparing the variation characteristics of energy dissipation with
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damage dissipation.
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material damage shown in Fig. 7, it can be reached that particle fracture dominates the
Fig. 8 Variations of (a) cutting force and (b) thrust force with cutting distance in cutting processes with four different DOCs.
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Fig. 9 Energy dissipation in PBX cutting with four DOCs. (a) Damage dissipation; (b) Frictional
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4 Conclusions
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dissipation; (c) Plastic dissipation; (d) Viscous dissipation.
In summary, we performed 2D FE simulations to elucidate cutting mechanisms involved
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in orthogonal cutting of HMX-based PBX. Based on a CFE framework, the material failure
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behavior including fracture of both crystal particles and binders, as well as debonding of particle-binder interfaces, were described by the implementation of cohesive elements. The HMX crystal particles shaped with proportionally-scaled Voronoi polygons has a particle volume fraction of 90%, and were modeled by a linear elasticity model. The HTPB binders were described by a rate-independent hyperelastic model coupled with a rate-dependent plasticity model. Simulation results revealed different interactions of crystal particles with tool edge, including fracture, pull out, squeeze out and push out of HMX crystal particles. While the laterally propagated crack finally led to formation of machined surface with high surface integrity, the longitudinally expanded crack eventually resulted into cavity formation. In particular for crystal particles residing on the cutting path, the failure mode s of crystal particles were closely associated with binder deformation. While friction dissipation and viscous dissipation were the main components of energy dissipation, the variation trend and
Journal Pre-proof size of external work were similar to friction loss and viscous loss. It was found that DOC has a strong impact on deformation behavior of PBX and correlated machining results. While cutting force increased with increasing DOC, a critical DOC of 0.4 mm for the best machined surface quality was found.
Acknowledgement The authors greatly acknowledge supports from the National Natural Science Foundation
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of China (grant number 51505441) and the Fundamental Research Funds for the Central
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Universities.
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Data Availability
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The raw/processed data required to reproduce these findings cannot be shared at this time
Reference
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Journal Pre-proof Credit Author Statement Jiaohu Huang: Conceptualization, Methodology, Supervision, Writing-Review & Editing; Shijin Lu: Software, Formal analysis, Visualization, Writing-Original Draft; Fengying Xie: Methodology, validation, Investigation, Writing-Original Draft; Wei Liu: Conceptualization,
Supervision;
Caiwei
Xiao:
Conceptualization,
Methodology,
Writing-Review & Editing, Project administration; Junjie Zhang: Conceptualization,
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Supervision, Resources, Writing-Review & Editing; Tao Sun: Supervision.
Journal Pre-proof Declaration of interests The authors declare that they have no known competing financial interests or personal
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relationships that could have appeared to influence the work reported in this paper.
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Graphical abstract
Journal Pre-proof Highlights Synergetic cutting mechanisms of PBX energetic material were revealed by cohesive finite element simulations for the first time. Cohesive elements were implemented to describe fracture of both crystal particles and binders, as well as debonding of particle-binder interface in PBX cutting. Crystal particles failure modes of fracture, pull out, squeeze out and push out, and their
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correlations with machined surface topography, were revealed.