Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Effect of tool geometry on ultraprecision machining of soft-brittle materials:a comprehensive review

Brittle materials are widely used for producing important components in the industry of optics,optoelectronics,and semiconductors.Ultraprecision machining of brittle materials with high surface quality and surface integrity helps improve the functional performance and lifespan of the components.According to their hardness,brittle materials can be roughly divided into hard-brittle and soft-brittle.Although there have been some literature reviews for ultraprecision machining of hard-brittle materials,up to date,very few review papers are available that focus on the processing of soft-brittle materials.Due to the‘soft’and‘brittle’properties,this group of materials has unique machining characteristics.This paper presents a comprehensive overview of recent advances in ultraprecision machining of soft-brittle materials.Critical aspects of machining mechanisms,such as chip formation,surface topography,and subsurface damage for different machining methods,including diamond turning,micro end milling,ultraprecision grinding,and micro/nano burnishing,are compared in terms of tool-workpiece interaction.The effects of tool geometries on the machining characteristics of soft-brittle materials are systematically analyzed,and dominating factors are sorted out.Problems and challenges in the engineering applications are identified,and solutions/guidelines for future R&D are provided.

Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression

Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

Is Mg_(17)Al_(12) ductile or brittle?A theoretical insight

The Mg_(17)Al_(12)-phase,which is common and important in Mg-Al alloy,has long been regarded as a brittle phase in experiments but theoretical calculations report controversial results.To unravel why theoretical calculations report controversial results and determine whether Mg_(17)Al_(12)is brittle or ductile,density functional theory calculations on atomic level are performed to investigate mechanic properties of Mg_(17)Al_(12)without containing alloying elements and without taking the size effect.The results showed that the parameter k-point played critical role in the DFT-based elastic calculations.The convergent G/B ratio of Mg_(17)Al_(12)was about 0.52,suggesting that the Mg_(17)Al_(12)-phase was theoretically ductile although its ductility was poor.The chemical bonding in Mg_(17)Al_(12)was the mixture of metallic Mg-Mg bond and covalent Al-Al bond.The advantage of metallic bonding over covalent bonding provided a possible explanation for the ductility of Mg_(17)Al_(12).Possible reasons for the brittleness of Mg_(17)Al_(12)in experiments are also discussed.

APPLICATION OF DIAMOND TWIST DRILL FOR DRILLING HARD-BRITTLE MATERIALS

A new conception, which combines the advantages of both twist drill and diamond grit, is proposed to develop a new tool for drilling hard brittle materials. The manufacturing process of the drill is introduced, and drilling experiments are carried out by using of the drill developed. As a result, not only it can drill holes with a high efficiency, but also a good quality of hole inlet and outlet can be obtained for such materials as glasses, marble, granite, Al 2O 3, etc. The prospect in practical application of the technique developed is also discussed.

DUCTILEBRITTLETRANSITION OF POLYCRYSTALLINE Ni_3Al WITH VARYING GRAIN SIZE

It is known that in B (un)doped Ni 3Al polycrystals, the dependence of yield strength on grain size follows the Hall Petch relationship: σ y= σ 0+ K y d -1/2 , and the slope K y can be reduced by B doping owing to the lowering of grain boundary resistance to slip transmission. If the intergranular cracking in polycrystalline Ni 3Al occurs from the microcavity along the grain boundaries, the effective external tensile stress for the propagation of the crack like microcavity along the grain boundaries can be deduced as: σ f= σ i+ K u d -1/2 , where K u reflects the effects of such factors as environment, strain rate, boron doping and the orientation of the grain boundary on the trend of intergranular cracking. For loaded polycrystalline Ni 3Al, it should be competitive between the intergranular cracking and slip transmission across the grain boundary. Therefore, comparing the varieties of both σ y and σ f with grain size, the dependence of ductile brittle transition on grain size, and the effects of the above factors on ductile brittle transition can be expected. The model also predicts that there exists a critical grain size for the ductile brittle transition of polycrystalline Ni 3Al alloys, and B doping can increase the critical grain size due to the reduction of the slope K y and the increase of K u. The reported experimental results verified the above model.

Rotary ultrasonic-assisted milling of brittle materials

In order to improve the machining efficiency of ultrasonic milling,the easiest and most effective approach was started with the improvement of tool design.The main objective of this research was to utilize rotary ultrasonic machining (RUM's) effectiveness in removing brittle materials to extend the applications of this independent,innovative manufacturing method (self-driving rotary ultrasonic machining),and to experimentally investigate its milling application on brittle materials.The designed tool was used in the conjunction with previously established RUM machine tools,and glass was selected as workpiece for experiments.The interrelationship between feed rate and depth of cut was discussed.By measuring the surface roughness of workpiece,the overall efficacy of utilizing RUM for milling was evaluated and presented.Ultrasonic assisted milling results in the reduction of milling resistance,which leads to a greater process rate.

Geochronology Constraints on Transformation Age from Ductile to Brittle Deformation of the Shangma Fault and Its Tectonic Significance,Dabieshan,Central China

By a detailed investigation of geometry and kinematics of the Shangma （商麻） fault in Dabieshan （大别山）, three different crust levels of extension movement have been recognized in sequence from the deep to the shallow：① low-angle ductile detachment shearing with top to the NW; ② low-angle normal fault with top to the NW or NWW in brittle or brittle-ductile transition domain; ③ high-angle brittle normal fault with top to the W or NWW. Two samples were chosen for zircon U-Pb age dating to constrain the activity age of the Shangma fault. A bedding intrusive granitoid pegmatite vein that is parallel to the foliation of the low-angle ductile detachment shear zone of the country rock exhibits a lotus-joint type of boudinage deformation, showing syn-tectonic emplacing at the end of the ductile deformation period and deformation in the brittle-ductile transition domain. The zircon U-Pb dating of this granitoid pegmatite vein gives an age of （125.9±4.2） Ma, which expresses the extension in the brittle-ductile transition domain of the Shangma fault. The other sample, which is collected from a granite pluton cutting the foliation of the low-angle ductile detachment shear zone, gives a zircon U-Pb age of （118.8±4.1） Ma, constraining the end of the ductile detachment shearing. Then the transformation age from ductile to brittle deformation can be constrained between 126-119 Ma. Combined with the previous researches, the formation of the Luotian （罗田） dome, which is locatedto the east of the Shangma fault, can be constrained during 150-126 Ma. This study gives a new time constraint to the evolution of the Dabie orogenic belt.

Modelling of spall damage in ductile materials and its application to the simulation of the plate impact on copper

A statistical model of dynamic spall damage due to void nucleation and growth is proposed for ductile materials under intense loading, which takes into account inertia, the elastic-plastic effect, and initial void size. To some extent, void interaction could be accounted for in this approach. Based on this model, the simulation of spall experiments for copper is performed by using the Lagrangian finite element method. The simulation results are in good agreement with experimental data for the free surface velocity profile, stress record behind copper target, final porosity, and void concentrations across the target. The influence of elastic-plastic effect upon the damage evolution is explored. The correlation between the damage evolution and the history of the stress near the spall plane is also analyzed.

Laser machining of transparent brittle materials: from machining strategies to applications

Transparent brittle materials such as glass and sapphire are widely concerned and applied in consumer electronics, optoelectronic devices, etc. due to their excellent physical and chemical stability and good transparency. Growing research attention has been paid to developing novel methods for high-precision and high-quality machining of transparent brittle materials in the past few decades. Among the various techniques, laser machining has been proved to be an effective and flexible way to process all kinds of transparent brittle materials. In this review, a series of laser machining methods, e.g. laser full cutting, laser scribing, laser stealth dicing, laser filament, laser induced backside dry etching (LIBDE), and laser induced backside wet etching (LIBWE) are summarized. Additionally, applications of these techniques in micromachining, drilling and cutting, and patterning are introduced in detail. Current challenges and future prospects in this field are also discussed.

Research on Ultrasonic Vibration Grinding of the Hard and Brittle Materials

It is well known that grinding techniques are main methods to machine hard and brittle materials such as engineering ceramics. But the conventional grinding has many shortcomings such as poorer surface finish, quicker wear and tear of grinding tools, lower efficiency and so on. Ultrasonic vibration grinding （UVG） which combines ultrasonic machining and grinding emerged as a developing and promising technique in recent years. In this paper, experimental studies on UVG were conducted on several kinds of hard and brittle material by altering processing parameters such as vibration frequency and its amplitude, diamond abrasive grit size, cutting depth, feeding speed and rotary speed of tools. The experimental results show that alteration in any of above mentioned parameters will bring effects on the processed surface finish of these materials. Of them, the diamond abrasive grit size has the greatest. Moreover, conventional grinding experiments were also carried out on these materials. By comparison, it was found that the UVG is superior to the conventional method in terms of the ground surface quality, the working efficiency and the wear rate of tools.

PROBABILISTIC MODELING OF BRITTLE FRACTURE WITH PRIOR DUCTILE CRACK EXTENSION

A computation framework for brittle fracture which incorporates weakest link statistics and a microme- chanics model reflecting reflecting local damage of the material is described.The Weibull stress W emerges as a probabilistic fracture parameter to define the condition leading material failure. Unstable crack propa- gation occurs at a critical value of W which may be attained paior to or following some amount of duc- tile crack extension. A realistic model of ductile crack growth using the computation cell methodology is used to define the evolution of near tip stress fields during crack extension. An application of proposed framework to predict the measured geometry and ductile tearing effects on the statistical distributio of fracture toughness for the pipe line steel welded joint is described.

QUASI-MICROMECHANICAL CONSTITUTIVE THEORY FOR BRITTLE DAMAGED MATERIALS UNDER TENSION

One of fundamental but difficult problems in damage mechanics isthe formulation of the ef- fective constitutive relation ofmicrocrack-weakened brittle o quasi-brittle materials under complexloading, especially when microcrack interaction is taken intoaccount. The combination of phenomenological and mi- cromechanicaldamage mechanics is a promising approach to construction andapplicable damage model with a firm physical foundation.

Mechanism of brittle-ductile transition of a glass-ceramic rigid substrate

The hardness, elastic modulus, and scratch resistance of a glass-ceramic rigid substrate were measured by nanoindentation and nanoscratch, and the fracture toughness was measured by indentation using a Vickers indenter. The results show that the hardness and elastic modulus at a peak indentation depth of 200 nm are 9.04 and 94.70 GPa, respectively. These values reflect the properties of the glass-ceramic rigid substrate. The fracture toughness value of the glass-ceramic rigid substrate is 2.63 MPa？m1/2. The material removal mechanisms are seen to be directly related to normal force on the tip. The critical load and scratch depth estimated from the scratch depth profile after scratching and the friction profile are 268.60 mN and 335.10 nm, respectively. If the load and scratch depth are under the critical values, the glass-ceramic rigid substrate will undergo plastic flow rather than fracture. The formula of critical depth of cut described by Bifnao et al. is modified based on the difference of critical scratch depth

Towards understanding the brittle–ductile transition in the extreme manufacturing

The brittle–ductile transition(BDT) widely exists in the manufacturing with extremely small deformation scale, thermally assisted machining, and high-speed machining. This paper reviews the BDT in extreme manufacturing. The factors affecting the BDT in extreme manufacturing are analyzed, including the deformation scale and deformation temperature induced brittle-to-ductile transition, and the reverse transition induced by grain size and strain rate. A discussion is arranged to explore the mechanisms of BDT and how to improve the machinability based on the BDT. It is proposed that the mutual transition between brittleness and ductility results from the competition between the occurrence of plastic deformation and the propagation of cracks. The brittleness or ductility of machined material should benefit a specific manufacturing process, which can be regulated by the deformation scale, deformation temperature and machining speed.

Optimization of Abrasive Water Jet Cutting of Ductile Materials

Full factorial design of experiments was developed in order to investigate the effects of jet pressure, abrasive mixing rate, cutting feed, and plate thickness upon three response variables, surface finish of cutting wear zone, percentage proportion of striation free area, and maximum width of cut. The set of sixteen experiments was performed on each of the following two ductile materials： AISI 4340 （high strength low alloy steel, hardened to 49HRc） and Aluminum 2219. Analysis of Variance （ANOVA） was performed on experimental data in order to determine the significance of effects of different parameters on the performance measures. It was found that cutting feed and thickness were highly influential parameters, while abrasive mixing rate is influential upon surface roughness only. Strong interaction was found between jet pressure and workpiece material. Multi-criteria numerical optimization was performed in order to simultaneously maximize/minimize different combinations of performance measures.

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),the micromechanisms of damage in quasi-brittle materials subjected to triaxial either tensile or compressive loading are investigated and the complete strew-strain relation including four stages is obtained from micromechanical analysis.The regime of pre-peak nonlinear hardening corresponds to the distributed damage,i.e.the stable propagation of microcracks.After the attainment of the ultimate strength of load-bearing capacity, some microcracks experience the second unstable growth and the distributed damage is transmitted to the localization of damage.These analyses improve our understanding of the hardening and softening behaviors of quasi-brittle materials.

Anisotropic brittle-ductile transition of monocrystalline sapphire during orthogonal cutting and nanoindentation experiments

Single-crystal sapphire is utilized as a high-performance engineering material,especially in extreme and harsh environments.However,due to its extreme hardness and brittleness,the machinability of sapphire is still a challenge.By means of nanoindentation and plunge-cut experiments,the anisotropic brittle-ductile transition of the prismatic M-plane and rhombohedral R-plane is examined by analyzing crack morphologies and the critical depth-of-cut(CDC).The experimental results of the nanoindentation tests are correlated to the plunge-cut experiment.Both the prism plane and the rhombohedral crystal plane exhibit a two-fold symmetry of ductility with various crack patterns along the machined grooves.The direction-dependent plasticity of the hexagonal sapphire crystal is mainly connected to a twinning process accompanied by slip dislocation.

EXPERIMENTAL STUDY OF MICROHOLE GROWTH AND COALFSCENCE IN DUCTILE MATERIALS

The growth and coalescence of two microholes in copper foil were studied experimental ly by in situ tensile tests under a,scanning electronic microscope.Two microholes of 15-35μm in di- ameter were arranged in different distances and orientations.It was found that the mechanisms of mi crohole evolution were represented by slipping band creation,and then crack initiation and propagation along the slipping bands,in ligament.The process of microhole growth and coalescence was influenced by the inter-center distance and orientation of microholes.The critical surface of microholes at coales- cence is about 2—2.5 times that of the initial one.The variation of both the inter center distance and orientation depends on the initial angle.

INVESTIGATION OF HYDROGEN INDUCED DUCTILE BRITTLE TRANSITION IN 7175 ALUMINUM ALLOY

Effects of hydrogen on the mechanical properties of differently aged 7175 aluminum alloys were investigated by using cathodic H-permeation, slow strain rate tension and so on. The results indicate that both the yield stress and the percentage reduction of area decrease with increasing hydrogen charging time, and the degree of reduction decreases as aging time increases for the same hydrogen charging time.