Simulation of dynamic response of granite: A numerical approach of shock-induced damage beneath impact craters

The mechanical response of rocks to dynamic loading is complex. It is not well understood because of the difficulty of defining an effective shear and tensile strength model. Recently AUTODYN-2D from Century Dynamics is used to simulate the shock-induced damage in granite targets impacted by projectiles at different velocities. The simulated results are compared with experiment data. Johnson–Holmquist shock damage constitutive model for brittle materials is applied to describe the damage and shear strain achieved in a confined volume of granite. A tensile crack softening model is coupled with the JH model to simulate the propagation of radial tensile cracks generated by the principal tensile stress perpendicular to the shock front. The tensile stress is assumed to be equal to the deviatoric stress at radii that experience less than the Hogoniot elastic limit stress. Instead of traditional grid-based methods, a smooth particle hydrodynamics is used to define damaged regions in brittle media.     

The relation of failure under 1D shock to the ballistic performance of brittle materials

The response of brittle materials to uniaxial compressive shock loading is still not well understood. Describing the physical mechanisms resulting from the more complex triaxial states that result from impact and penetration is thus empirical. The physical interpretation of the yield point of brittle materials in one-dimensional strain (the Hugoniot elastic limit (HEL)), the rate dependence of this threshold, the form of stress histories and the effect of polycrystalline microstructure still remain to be comprehensively explained. However, evidence of failure occurring in glasses and ceramics behind a travelling front that follows a shock front has been accumulated and verified in several laboratories. Such a boundary has been called a failure front. The variations in properties across this front include complete loss of tensile strength, partial loss of shear strength, reduction in acoustic impedance, lowered sound speed and opacity to light. It is the object of this work to collect observations of these phenomena and their relation to failure and the HEL in brittle materials. Further, to relate these uniaxial strain measurements of their failed states to the depth of penetration (DoP) in the widely conducted test.     

Strength size effects and fracture mechanics: What does the physical evidence say?

Being able to predict the strength of geometrically-similar cracked specimens of different sizes or scales is a fundamental requirement for success for linear elastic fracture mechanics (LEFM). The prediction contained in LEFM is that the strength reduces as the inverse square-root of the scale factor in the plane of the crack: here we review how well this prediction actually agrees with the physical evidence. In particular we examine agreement for materials and configurations exhibiting brittle responses—the situations complying best with the underlying linear elastic assumptions in the theory. The data show that the agreement is not good, even in the most brittle of instances.     

Numerical simulation of elastic plastic fatigue crack growth in functionally graded material using the extended finite element method

In the present work, the extended finite element method has been used to simulate the fatigue crack growth problems in functionally graded material in the presence of holes, inclusions, and minor cracks under plastic and plane stress conditions for both edge and center cracks. Both soft and hard inclusions have been implemented in the problems. The validity of linear elastic fracture mechanics theory is limited to the brittle materials. Therefore, the elastic plastic fracture mechanics theory needs to be utilized to characterize the plastic behavior of the material. A generalized Ramberg-Osgood material model has been used for modeling purposes.     

Why do cracks branch? A peridynamic investigation of dynamic brittle fracture

In this paper we review the peridynamic model for brittle fracture and use it to investigate crack branching in brittle homogeneous and isotropic materials. The peridynamic simulations offer a possible explanation for the generation of dynamic instabilities in dynamic brittle crack growth and crack branching. We focus on two systems, glass and homalite, often used in crack branching experiments. After a brief review of theoretical and computational models on crack branching, we discuss the peridynamic model for dynamic fracture in linear elastic–brittle materials. Three loading types are used to investigate the role of stress waves interactions on crack propagation and branching. We analyze the influence of sample geometry on branching. Simulation results are compared with experimental ones in terms of crack patterns, propagation speed at branching and branching angles. The peridynamic results indicate that as stress intensity around the crack tip increases, stress waves pile-up against the material directly in front of the crack tip that moves against the advancing crack; this process “deflects” the strain energy away from the symmetry line and into the crack surfaces creating damage away from the crack line. This damage “migration”, seen as roughness on the crack surface in experiments, modifies, in turn, the strain energy landscape around the crack tip and leads to preferential crack growth directions that branch from the original crack line. We argue that nonlocality of damage growth is one key feature in modeling of the crack branching phenomenon in brittle fracture. The results show that, at least to first order, no ingredients beyond linear elasticity and a capable damage model are necessary to explain/predict crack branching in brittle homogeneous and isotropic materials.     

Fracture initiation in elastic brittle materials having non-linear fracture envelopes

A theory is outlined for determining the initiation of fracture and initial fracture propagation in elastic brittle materials having non-linear Mohr fracture envelopes. This theory is applied to a specific boundary value problem, i.e. a truncated quarter plane with arbitrary traction distribution on the truncated boundary and varying confining pressure. This problem simulates the chipping phase of the penetration of a wedge shaped tool into an elastic brittle material. Numerical results are obtained for two rock materials, Blair dolomite and quartzite. Results indicate that for increasing confining pressure, a limit condition is reached for both fracture initiation location and force. This limit location is closer to the boundary than the fracture initiation points at lower confining pressures, indicating smaller chips. It is also found that initial fracture propagation is less clearly defined at higher confining pressures. Both of these results have been observed experimentally.     

Ductile-to-brittle transition in tensile failure due to shear-affected zone with a stress-concentration source: a comparative study on punched-plate tensile-failure characteristics of precipitation-hardened and dual-phase steels

The effect of shear-affected zone (SAZ), with a stress-concentration source induced by the punching process, on tensile properties was investigated. Tests using honed specimens (which have the same shapes and stress-concentration without any SAZ) and smooth specimens were conducted to compare the effect with that of the punched specimens. Dual-phase steel, which has a high work-hardening ability and low yield strength, and precipitation-hardened steel, which has a low work-hardening ability and high yield strength, were used in the tests. Materials with two tensile strength grades were prepared from both types of steel. Only the precipitation-hardened steel with higher strength grade punched specimen showed a brittle fracture with extremely short fracture-elongation, whereas the other specimens showed a ductile fracture. The fracture surface analysis revealed that cracks initiated in the maximum shear stress plane of the SAZ under tensile loading at first. We call the crack “shear crack.” The steel which showed brittle fracture used in this study easily exhibited plastic-strain localization compared with the other steels. If the shear crack is sharp, then the transition from ductile to brittle failure tends to occur. Furthermore, the strength characteristics of the punched specimen depend on the crack length dependency of the strength resistance and the failure phenomenon of the original material.     

The damage and failure of GRP laminates by underwater explosion shock loading

This paper examines the development of microstructural damage in a glass-reinforced polymer (grp) laminate subjected to explosive shock loading in water. GRP is commonly used in small naval vessels, and may be subjected to underwater explosions. In the experiments, the laminates were exposed to increasing amounts of shock loading produced by underwater explosions. The laminates were backed with either water or air to modify the amount of bending experienced under loading, with the air-backed laminates having the higher amount of bending. Examination of the grp microstructure by optical and scanning electron microscopy after shock testing failed to reveal any damage to either the polymer matrix or glass fibres when the laminate was backed with water. In contrast, when the laminate was backed with air, small cracks were produced in the polymer matrix at low shock pressures. Raising the shock pressure above a threshold limit caused complete failure of the laminate by cracking in the polymer matrix, cracking of the glass fibres, and delamination of the glass fibres from the polymer. The differences in the shock resistance of the water- and air-backed grp are discussed. Measurements of the residual tensile fracture strength of the laminates after shock loading are also presented. The fracture strength of the water-backed laminate was not affected by shock, but the fracture strength of the air-backed laminate deteriorated with the onset of glass fibre breakage and delamination in the grp microstructure.     

Critical stress diagrams for brittle materials with defects of the cusped void/crack type

An analysis of the strength of a brittle solid with defects of the hypocycloid void/crack type in plane stress state is presented. Based on the tenets of the theory of equilibrium cracks, critical stress diagrams for a brittle material with defects of this type are constructed and compared with published experimental data. It is shown that, using a model of a brittle material with defects of the cusped void/crack type, it is possible to describe laws governing the fracture of certain materials.     

Stellite12钴基合金的疲劳性能及其断裂机理研究

采用三点弯曲疲劳法测得光滑试样和直缺口试样的S-N曲线以研究Stellite12钴基合金的疲劳性能,并通过断口形貌观察进一步探究该钴基合金的断裂过程。结果表明:光滑试样的疲劳极限为545 MPa,约为原始抗弯强度1552 MPa的25.4%;直缺口试样的疲劳极限约为101MPa,约为静态抗弯强度517.6MPa的19.1%。对于疲劳敏感性,光滑试样与直缺口试样的疲劳敏感性分别为397和31。此外发现疲劳裂纹多萌生于近表层聚集的碳化物处,同时表面缺陷也可诱发疲劳裂纹的萌生。疲劳裂纹的扩展主要表现为碳化物的穿晶断裂,钴基体在应力比R=0.1的疲劳加载条件下虽表现出一定的韧性且呈现出较多的撕裂脊,但也呈现出一定的脆性断裂模式,因此疲劳裂纹扩展模式为真疲劳与静态疲劳的混合模式。     

Shock-wave compression of brittle solids

Extensive experimental investigation in the form of large-amplitude, nonlinear wave-profile measurements which manifest the shock strength and equation-of-state properties of brittle solids has been performed. Brittle materials for which a base of dynamic property data is available include Al₂O₃, AlN, B₄C, CaCO₃, SiC, Si₃N₄, SiO₂ (quartz and glass), TiB₂, WC and ZrO₂. Planar impact methods and velocity interferometry diagnostics have been used exclusively to provide the high-resolution shock-profile data. These wave-profile data are providing engineering dynamic strength and equation-of-state properties as well as controlled, shock-induced motion histories for the validation of theoretical and computational models. Of equal importance, such data are providing a window into the physics of a newly emerging understanding of the compression and deformation behavior of high-strength brittle solids. When considered along with a rich assortment of strength and deformation data in the literature, a systematic assessment of this shock-wave data lends strong support for failure waves and concomitant high-confinement dilatancy as a general mechanism of inelastic deformation in the shock compression of ceramics. Phase transformation in selected brittle solids appears to be a critical state phenomenon strongly controlled by kinetics. The risetime and structure of deformation shock waves in brittle solids are controlled by viscous effects which at present are still poorly understood. The shock-wave data also suggest that both crystalline plasticity and brittle fracture may play important and interconnected roles in the dynamic failure process.     

Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading

Fatigue and brittle fracture propagation paths of arbitrary plane cracks, loaded in mode I, embedded in an infinite isotropic elastic body, are investigated. The crack advance is supposed to be governed by the stress intensity factor, for instance through Paris' law in fatigue or Irwin's criterion in brittle fracture. The method used is based on successive iterations of the three-dimensional weight-function theory of Bueckner-Rice, that gives the variation of the stress intensity factor along the crack front arising from some small arbitrary coplanar perturbation of the front. Its main advantage is that only one dimensional integrals along the crack front are involved so that only the one dimensional meshing of the crack front is needed, and not the 3D meshing of the whole body as in the finite-element method. It is closely linked to previous works of Bower and Ortiz (1990, 1991, 1993). The differences lie on the one hand, in the simplified numerical implementation; on the other hand, in the simplified treatment of brittle fracture, Irwin's criterion being regularized by Paris' law by a procedure analogous to the `viscoplastic regularization' in plasticity; and finally in the applications studied: propagation paths of an initially elliptical, rectangular or heart shaped crack in an homogeneous media and of a penny shape crack in an heterogeneous one.     

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

Special features of dynamic fracture of brittle materials in the mode of ultimate fracture velocities

Based on the model of spherical cavity expansion in brittle materials, which involves the concept of ultimate fracture velocities, we consider a stress-strain state in the elastic precursor zone and in the region of material broken by radial cracks. We have noted the mechanical effects of dynamic overload and fracture retardation, which arise within this model. Institute of Problems of Materials Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 20–26, March–April, 2000.     

What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation?

Criteria for predicting initiation of cracks in brittle materials like ceramics are based on two parameters: the material fracture toughness and the tensile strength. Standardized experiments exist to estimate the former. However, the tensile strength is often taken from experiments (mainly uniaxial bending) on specimens with various geometries and surface finish, usually tested under ambient conditions at a given loading rate. The reported strength is commonly the Weibull characteristic strength, which scatters due to the critical defect size distribution on the tested specimen. In this work, we propose a definition of the “inherent” or “intrinsic” tensile strength to be used in numerical models, making a distinction between extrinsic defects due to manufacturing and intrinsic ones relying on the microstructure. Our approach is based on the Finite Fracture Mechanics theory and the Coupled Criterion applied to small surface flaws and its influence on the measured (extrinsic) strength. Numerical results are compared with experiments on alumina reported in the literature. In addition, a model for the Petch law (strength vs. grain size) in polycrystalline materials is proposed using the Coupled Criterion, which predicts an initial crack length of increasing numbers of grains as the grain size decreases.     

Shock and release of polycarbonate under one-dimensional strain

The behaviour of the thermoplastic polycarbonate has been investigated using manganin stress gauges in both longitudinal and lateral orientations. These have been used to determine the shock stress, shock velocity, particle velocity, release velocity and shear strength. The relationship between shock velocity and particle velocity has been shown to be linear, with the value of c₀ (the zero particle velocity intercept of shock velocity) equating to the measured bulk sound speed. This behaviour is more commonly observed in metals. Shear strength has been observed to increase behind the shock front, a feature observed in other polymers such as PMMA or PEEK. It also increases with stress amplitude, although the projected intercept with the calculated elastic response indicates that the Hugoniot elastic limit (HEL) is lower than in other polymers, for example PMMA (ca. 0.75GPa) or PEEK (ca. 1.0GPa). This further suggests that the yield strength of polycarbonate does not obey a Mohr-Coloumb criterion, and hence is not as strongly pressure dependent as other polymers.     

The fracture mechanics of finite crack extension

This paper describes a modification to the traditional Griffith energy balance as used in linear elastic fracture mechanics (LEFM). The modification involves using a finite amount of crack extension (Δa) instead of an infinitesimal extension (da) when calculating the energy release rate. We propose to call this method finite fracture mechanics (FFM). This leads to a change in the Griffith equation for brittle fracture, introducing a new term Δa/2: we denote this length as L and assume that it is a material constant. This modification is extremely useful because it allows LEFM to be used to make predictions in two situations in which it is normally invalid: short cracks and notches. It is shown that accurate predictions can be made of both brittle fracture and fatigue behaviour for short cracks and notches in a range of different materials. The value of L can be expressed as a function of two other material constants: the fracture toughness K_c (or threshold ΔK_th in the case of fatigue) and an inherent strength parameter σ₀. For the particular cases of fatigue-limit prediction in metals and brittle fracture in ceramics, it is shown that σ₀ coincides directly with the ultimate tensile strength (or, in fatigue, the fatigue limit), as measured on plain, unnotched specimens. For brittle fracture in polymers and metals, in which larger amounts of plasticity precede fracture, the approach can still be used but σ₀ takes on a different value, higher than the plain-specimen strength, which can be found from experimental data. Predictions can be made very easily for any problem in which the stress intensity factor, K is known as a function of crack length. Furthermore, it is shown that the predictions of this method, FFM, are similar to those of a method known as the line method (LM) in which failure is predicted based on the average stress along a line drawn ahead of the crack or notch.