Crack arrest in elastic sheets

The analysis of the motion of a crack of finite length extending in an infinite isotropic elastic sheet loaded in the extensional mode forms the basis for the treatment of the motion and the arrest of a brittle crack in a more general two-dimensional structure of finite size. The energy flow to the cracktip is expressed in terms of the value of the static J-integral times a dynamic function depending on the instantaneous crack-tip velocity. This energy flow is equal to the fracture energy which is supposed to be a specific function only of the crack-tip velocity for a given material. If the energy release (calculated as described) becomes less than the fracture energy in some segment along the prospective fracture path, then additional energy will be needed for the crack to be propagated. Such additional energy is available owing to the kinetic state of the structure. An upper limit to the amount of additional energy is determined. A conservative crack-arrest condition is given by the assumption that all this additional energy is consumed in a continued slow extension of the crack. Experimental results for edge-cracked sheets of polymethylmethacrylate conform well with the crack-arrest condition suggested.     

Effects of near-tip rotation on pre-buckle crack growth of compressed beams bonded to a rigid substrate

The macroscopic pre-cracked line scratch test (MPLST), in which a debonded edge of a film is loaded in in-plane compression, has been modeled as a generic, coupled fracture–buckle problem using simple beam theory. Near crack-tip beam rotation (also called root rotation in literature), which always exists due to the eccentric loading in this type of test, has been incorporated into the governing equations. An analytical solution to the augmented problem has been derived. It is found that the near-tip rotation can introduce pre-buckle bending in the film. One important consequence of this pre-buckle bending is that it leads to the reduction of the critical buckling condition. This agrees well with the results of [Int. J. Fract. 113 (2002) 39] obtained by solving the full elastic field near the crack-tip. Furthermore, the pre-buckle bending moment at crack-tip remains negative (leading to crack closure) as long as the pre-buckle crack length is small, but it becomes positive (leading to crack opening) at larger pre-buckle crack length. The negative bending moment causes the crack-tip energy release rate to decrease as the crack propagates, which results in a stable pre-buckle crack growth. Once it becomes positive, however, the bending moment causes crack-tip energy release rate to increase rapidly as crack length increases and hence leads to an unstable (pre-buckle) crack growth. Further, the nominal phase angle is initially larger than the classic prediction of 52.1° owing to the existence of the negative crack-tip bending moment, but it drops quickly upon approaching the buckle point. All these results are confirmed by a rigorous 2D FEM calculation using cohesive zone modeling (CZM) approach. Finally the derived analytical solution has been used to analyze a set of PLST data reported in the literature. It has been demonstrated that plasticity in the adhesive layer and in the bonded film is responsible for the strong R-curve toughening characteristics in the deduced interface toughness data. It has also been shown that, once the deduced interface toughness is incorporated into a CZM simulation, both the axial loading and buckling point can be accurately predicted.     

Crack propagation in an elastic solid subjected to general loading—III. Stress wave loading

The stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to stress wave loading is determined. A plane stress pulse strikes the crack at time t = 0, the wavefront being parallel to the plane of the crack. At some arbitrary later time t = τ, the crack begins to extend at a non-uniform rate. It is found that the stress intensity factor is a universal function of instantaneous crack-tip velocity times the stress intensity factor for an equivalent stationary crack. An energy rate balance fracture criterion is applied to obtain an equation of motion for the crack tip. The delay time between the arrival of the incident pulse and the onset of fracture is also calculated for this fracture criterion.     

An electrically impermeable and magnetically permeable interface crack with a contact zone in magnetoelectroelastic bimaterials under a thermal flux and magnetoelectromechanical loads

An interface crack with a frictionless contact zone at the right crack-tip between two dissimilar magnetoelectroelastic materials under the action of a thermal flux and remote magnetoelectromechanical loads is considered. The open part of the crack is assumed to be electrically impermeable and magnetically permeable, and the crack faces are assumed to be heat insulted. The inhomogeneous combined Dirichlet–Riemann and Hilbert boundary value problems are, respectively, formulated and solved analytically. Stress, electrical displacement intensity factors as well as energy release rate are found in analytical forms, and analytical expressions for the contact zone length have been obtained for both the general case and the case of small contact zone length. Some numerical results are presented, which show clearly the effects of thermal and magnetoelectromechanical loads on the contact zone length, stress intensity factor and energy release rate. Results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures and devices.     

On the driving force for crack growth during thermal actuation of shape memory alloys

The effect of thermomechanically induced phase transformation on the driving force for crack growth in polycrystalline shape memory alloys is analyzed in an infinite center-cracked plate subjected to a thermal actuation cycle under mechanical load in plain strain. Finite element calculations are carried out to determine the mechanical fields near the static crack and the crack-tip energy release rate using the virtual crack closure technique. A substantial increase of the energy release rate – an order of magnitude for some material systems – is observed during the thermal cycle due to the stress redistribution induced by large scale phase transformation. Thus, phase transformation occurring due to thermal variations under mechanical load may result in crack growth if the crack-tip energy release rate reaches a material specific critical value.     

Intersonic crack propagation along interfaces: Experimental observations and analysis

The isochromatic fringe patterns surrounding an intersonically propagating interface crack are developed and characterized using the recently developed stress field equations. A parametric investigation is conducted to study the influence of various parameters such as the crack-tip velocity and the contact coefficient on the isochromatic fringe patterns. It has been observed that the crack-tip velocity has a significant effect on the size and shape of isochromatic fringe patterns. The contact coefficient, on the other hand, does not affect the fringe pattern significantly. The paper also presents a numerical scheme to extract various parameters of interest such as the series coefficients of the stress field, the contact coefficient and the dissipation energy. The results show that the crack growth is highly unstable in the intersonic regime, and the energy dissipation decreases monotonically with increasing crack-tip velocity. The experimental data fit well with the recently proposed fracture criterion for intersonic interfacial fracture.     

Dynamic crack propagation in a magneto-electro-elastic solid subjected to mixed loads: Transient Mode-III problem

The transient response of a Mode-III crack propagating in a magneto-electro-elastic solid subjected to mixed loads is investigated through solving the corresponding boundary-initial-value problem in both the cracked solid region and the interior fluid region with treatment of electro-magnetically permeable and impermeable crack face conditions in a unified way. The closed-form results for the dynamic field intensity factors are used to evaluate the dynamic energy release rate through the crack-tip dynamic contour integral. The permeability of the interior fluid region relative to the cracked solid region significantly affects the magneto-electro-mechanical coupling coefficient in the Bleustein–Gulyaev wave function and, consequently, the horizontal shear surface wave speed, the dynamic field intensity factors and the dynamic energy release rate. It is revealed from dynamic fracture mechanics analysis that the dynamic energy release rate thus obtained has an odd dependence on the dynamic electric displacement intensity factor and the dynamic magnetic induction intensity factor. It is also found that the horizontal shear surface wave speed provides the limiting velocity for the propagation of a Mode-III crack in a magneto-electro-elastic solid when there is only applied traction loading.     

裂纹面摩擦接触引起的断裂韧性增长的研究

采用弹黏塑性的材料本构关系, 建立了压、剪混合型裂纹常速准静 态扩展的力学模型, 求得了裂纹面摩擦接触条件下裂纹尖端场的数值解, 并基于数 值结果讨论了扩展裂纹的摩擦效应. 计算和分析表明, 裂纹面的摩擦效应主要表现 在两个方面. 第一方面是摩擦会导致裂纹尖端区材料的断裂韧性增高, 并且裂纹面间的摩擦作用越强, 增韧效果越显著. 摩擦增韧的机制可以解释为裂纹 面间的摩擦作用导致裂纹尖端塑性区尺寸变大, 使裂纹尖端场的塑性变形能增加, 从而使得裂纹尖端区材料增韧. 摩擦生热并不是导致材料断裂韧性增长的根本机制. 第二方面是摩擦会导致``断裂延缓'. 利用裂纹面的摩擦来提高构件的承载能力和延长构件的服役寿命具有较大的工程实用价值.     

Effects of surface diffusion and resolved shear stress intensity factor on environmentally assisted cracking

Hydrogen induced crack-tip plastic deformation has been known as the primary mechanism of hydrogen assisted cracking and stress corrosion cracking. It has been systematically shown that the same mechanism of environmentally assisted crack-tip dislocation emission causes hydrogen assisted cracking, stress corrosion cracking, and liquid metal embrittlement cracking.An embrittling chemical species has to reach a crack tip in order to accelerate crack growth. Very close to a sharp crack tip, surface diffusion is shown to be the dominant transport process of embrittling species for stage-II crack growth. The role of surface diffusion in stage II crack growth is analyzed. The constant cracking velocity is proportional to the surface diffusion coefficient of an embrittling species and inversely proportional to a length parameter, , which is related to the transport process upstream.Dislocation emission at a crack tip is driven by crack-tip resolved shear stress. Crack-tip resolved shear stress field is characterized by resolved shear stress intensity factor, K_RSS·K_RSS is defined, the procedure for its calculation outlined, and its applications to crack-tip dislocation emission and environmentally assisted cracking discussed.     

Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

Field structure at mode Ⅲ dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

Analysis of energy release rate for cracked laminates

1.IntroductionFailurebehaviorofcompositematerialsandsomeothermaterialslikewoodsandorientedpolymersaregovernedbyanisotropicandheterogeneouscharacteristics(Suoetal.,l99l,O'Brien,l987)I"21.ltiswell-knownthattheelasticstressfieldatthecracktiphasaninversesquarerootsingularityforgenerallyanisotropicbuthomogeneousmaterials(Hoenig,1982)l,l.ForheterogeneousmatCrials,aslongastheelasticmoduliarecontinuousanddifferentiablefunctionsofthespatialcoordinates,thisinversesquarerootsingularitystillprevails(Eis…     

受载高聚物裂尖的损伤和银纹化

采用扫描电子显微镜(SEM)，对高聚物裂尖银纹损伤的引发和演化过程进行了原位观测．将固态高聚物本体材料视为线黏弹体，裂尖银纹区视为非线性损伤区，通过构造银纹区的损伤演化方程，给出了银纹区应力模型和银纹生长规律，数值结果与已有实验吻合良好。     

An integral equation method in dynamic fracture mechanics

This paper contains a study of the problems of crack propagation under static stresses and under transient stress waves. Within the assumption of linear elastic fracture mechanics, an integral-equation method has been developed for the analysis of these problems. The method has been applied to: (a) the determination of the stress intensity factor at a given loading and a crack-tip velocity and (b) the determination of the crack-tip motion under a given transient loading.     

Transient crack growth under creep conditions

Transient crack growth in an elastic/power-law creeping material is investigated under antiplane shear loading and small-scale-yielding conditions. At time t = 0 the solid is suddenly loaded far from the crack by tractions that correspond to the elastic crack-tip stress distribution. At that time the crack begins to propagate at a constant velocity. The stress fields evolve in a complex manner as the crack propagates due to the competing effects of stress relaxation due to constrained creep and stress elevation due to the instantaneous elastic material response to crack growth. From detailed finite element calculations it is shown that these fields can be approximated by a simple matching of three asymptotic singular crack-tip solutions. A characteristic stress, distance and time are defined for this problem which provide a normalization that accounts for any crack velocity, loading and all material properties for a given creep exponent n. Results are presented for crack-tip stresses, strains, crack opening displacements and creep zones.     

压-剪混合型定常扩展裂纹尖端的弹黏塑性场

假定黏性系数与塑性等效应变率的幂次成反比,考虑其黏性和裂纹面摩擦接触效应 建立了压-剪混合型定常扩展裂纹尖端弹黏塑性场的渐近方程,求得了裂纹尖端场不含应力、应变间 断的数值解. 并讨论了压-剪混合型裂纹数值解随各个参数的变化规律,计算结果 和分析表明,压-剪混合型裂纹尖端场是满塑性的,不含有弹性卸载区,黏性效应是研究扩展裂纹尖端场时的一个重要因素. 无论混合裂纹趋近I型还是趋近II型,静水压力随摩擦系数的增加都是增加的,裂纹面摩擦 效应是阻止裂纹扩展速度的因素,且摩擦作用越强,裂纹尖端场的韧性越高.     

Dynamic fracture instabilities in brittle crystals generated by thermal phonon emission: Experiments and atomistic calculations

Dynamic cleavage fracture experiments of brittle single crystal silicon revealed several length scales of surface and path instabilities: macroscale path selection, mesoscale crack deflection, and nanoscale surface ridges. These phenomena cannot be predicted or explained by any of the continuum mechanics based equations of motion of dynamic cracks, as presumably critical energy dissipation mechanisms are not fully accounted for in the theories. Experimentally measured maximum crack speed, always lower than the theoretical limit, is another phenomenon that is as yet not well understood.We suggest that these phenomena depend on velocity dependent and anisotropic material property that resists crack propagation. The basic approach is that the bond breaking mechanisms during dynamic crack propagation vibrate the atoms at the crack front to generate thermal phonon emission, or heat, which provides additional energy dissipation mechanisms. This energy dissipation mechanism is a material property that resists crack propagation. To evaluate this property, we combined the continuum based elastodynamic Freund equation of motion with molecular dynamics atomistic computer “experiments”.We analyzed the above experimental dynamic fracture instabilities in silicon with the obtained velocity dependent and anisotropic material property and show its importance in cleavage of brittle crystals.     

Combination of fracture and damage mechanics for numerical failure analysis

A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J-integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.     

Dynamics of crack penetration vs. branching at a weak interface: An experimental study

In this paper, the dynamic crack-interface interactions and the related mechanics of crack penetration vs. branching at a weak interface are studied experimentally. The interface is oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. The focus of this investigation is on the effect of interface location and the associated crack-tip parameters within the bilayer on the mechanics of the ensuing fracture behavior based on the optical methodologies laid down in Ref. Sundaram and Tippur (2016). Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories in different bilayer configurations is performed using Digital Gradient Sensing (DGS) technique in conjunction with high-speed photography. The results show that the crack path selection at the interface and subsequently the second layer are greatly affected by the location of the interface within the geometry. Using optically measured fracture parameters, the mechanics of crack penetration and branching are explained. Counter to the intuition, a dynamically growing mode-I approaching a weak interface at a lower velocity and stress intensity factor penetrates the interface whereas a higher velocity and stress intensity factor counterpart gets trapped by the interface producing branched daughter cracks until they kink out into the next layer. An interesting empirical observation based on measured crack-tip parameters for crack penetration and branching is also made.     

The sliding interface crack with friction between elastic and rigid bodies

The paper analyzes the frictional sliding crack at the interface between a semi-infinite elastic body and a rigid one. It gives solutions in complex form for non-homogeneous loading at infinity and explicit solutions for polynomial loading at the interface. It is found that the singularities at the crack tips are different and that they are related to distinct kinematics at the crack tips. Firstly, we postulate that the geometry of the equilibrium crack with crack-tip positions b and a is determined by the conditions of square integrable stresses and continuous displacement at both crack tips. The crack geometry solution is not unique and is defined by any compatible pair (b,a) belonging to a quasi-elliptical curve. Then we prove that, for an equilibrium crack under given applied load, the “energy release rate” G_tip, defined at each crack tip by the J_ε-integral along a semi-circular path, centered at the crack tip, with vanishing radius ε, vanishes. For arbitrarily shaped paths embracing the whole crack, with end points on the unbroken zone, the J-integral is path-independent and has the significance of the rate, with respect to the crack length, of energy dissipated by friction on the crack.