A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.     

A critical shear displacement criterion for ductile–brittle transition under mixed mode I and II loading

Abstract

Micromechanisms producing ductile and brittle damage operate in parallel at a crack tip. The dominant mode of failure depends upon which of the two (ductile or brittle) damage parameters first reaches its critical value. This has been shown by a study of ductile–brittle transition behaviour in HY100 steel under mixed mode I and II loading. The transition from ductile to brittle behaviour in HY100 steel was found to be affected by mixed mode I and II ratio (ratio of imposed tensile and shear loading) in a manner such that with increasing shear the transition temperature decreased. In the present paper, a criterion is proposed based on the shear strain ahead of a notch tip, to predict the fracture behaviour at any given temperature and mixed mode ratio.     

An analysis of dynamic,ductile crack growth in a double edge cracked specimen

Dynamic crack growth is analysed numerically for a plane strain double edge cracked specimen subject to symmetric impulsive tensile loading at the two ends. The material behavior is described in terms of an elastic-viscoplastic constitutive model that accounts for ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second phase particles are represented, including large inclusions or inclusion colonies with low strength, which result in large voids near the crack tip at an early stage, and small second phase particles, which require large strains before cavities nucleate. The crack growth velocities determined here are entirely based on the ductile failure predictions of the material model, and thus the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Different prescribed impact velocities, inclusion spacings and values of the inclusion nucleation stress are considered. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed.     

Dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.     

Ratchetting strain as a damage parameter in controlling crack growth at elevated temperature

Progressive increase in tensile strains near a crack tip has been observed from finite element studies of stationary and growing cracks (Zhao, 2004, 2008) [1] and [2] under cyclic loading conditions. In this work, the significance of such a phenomenon was further explored. In particular, stress-controlled experiments were carried out to evaluate the uniaxial ratchetting response of a nickel-based superalloy, and the material parameters were re-calibrated using both strain-controlled and stress-controlled experimental data. An additional kinematic hardening term was introduced in the viscoplastic constitutive model and the models were utilised via a user-defined subroutine to study near crack tip ratchetting behaviour of a single edge notch tension (SENT) model geometry at elevated temperature. Loading modes near the crack tip were examined, together with the influence of particular constitutive models on the mechanistic response of the crack tip. The crack tip deformation was found to be predominantly strain-controlled, where the mean ratchetting strain seems to be more relevant to crack growth than the strain range. The former was used as a measure of crack tip damage to correlate crack growth rates at selected loading conditions.     

Finite deformation cohesive polygonal finite elements for modeling pervasive fracture

In the present study, mode I crack subjected to cyclic loading has been investigated for plastically compressible hardening and hardening–softening–hardening solids using the crack tip blunting model where we assume that the crack tip blunts during the maximum load and re-sharpening of the crack tip takes place under minimum load. Plane strain and small scale yielding conditions have been assumed for analysis. The influence of cyclic stress intensity factor range (\(\Delta \hbox {K})\), load ratio (R), number of cycles (N), plastic compressibility (\({\upalpha })\) and material softening on near tip deformation, stress–strain fields were studied. The present numerical calculations show that the crack tip opening displacement (CTOD), convergence of the cyclic trajectories of CTOD to stable self-similar loops, plastic crack growth, plastic zone shape and size, contours of accumulated plastic strain and hydrostatic stress distribution near the crack tip depend significantly on \(\Delta \hbox {K}\), R, N, \({\upalpha }\) and material softening. For both hardening and hardening–softening–hardening materials, yielding occurs during both loading and unloading phases, and resharpening of the crack tip during the unloading phase of the loading cycle is very significant. The similarities are revealed between computed near tip stress–strain variables and the experimental trends of the fatigue crack growth rate. There was no crack closure during unloading for any of the load cycles considered in the present study.     

Localized fracture phenomena in thermo-visco-plastic flow processes under cyclic dynamic loadings

Summary The main objective of the paper is the investigation of localized fatigue fracture phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings. Recent experimental observations for cycle fatigue damage mechanics at high temperature and dynamic loadings of metals suggest that the intrinsic microdamage process does very much depend on the strain rate and the wave shape effects and is mostly developed in the regions where the plastic deformation is localized. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process.A general constitutive model of elasto-viscoplastic damaged polycrystalline solids developed within the thermodynamic framework of the rate type covariance structure with a finite set of the internal state variables is used (cf. Dornowski and Perzyna [16], [17], [18]). A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic nonnormality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms (nucleation, growth and coalescence of microcracks); (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity; (vi) plastic spin.To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during a dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elasticplastic response can be obtained. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focussed on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. The Lax-Richtmyer equivalence theorem is formulated, and conditions under which this theory is valid are examined. Utilizing the finite difference method for a regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented.Particular examples have been considered, namely a dynamic adiabatic cyclic loading process for a thin plate with sharp notch. To the upper edge of the plate is applied a cyclic constraint realized by rigid rotation of the edge of the plate while the lower edge is supported rigidly. A small localized region, distributed asymmetrically near the tip of the notch, which undergoes significant deformation and temperature rise, has been determined. Its evolution until occurrence of fatigue fracture has been simulated.The propagation of the macroscopic fatigue damage crack within the material of the plate is investigated. It has been found that the length of the macroscopic fatigue damage crack distinctly depends on the wave shape of the assumed loading cycle.     

Simulation of brittle and ductile fracture in an impact loaded prenotched plate

We analyze the initiation and propagation of a crack from a point on the surface of a circular notch-tip in an impact loaded prenotched plate. The material of the plate is assumed to exhibit strain hardening, strain-rate hardening, and softening due to the rise in temperature and porosity. The degradation of material parameters due to the evolution of damage in the form of porosity is considered. Brittle failure is assumed to initiate when the maximum tensile principal stress at a point reaches a critical level. Ductile failure is assumed to ensue when the effective plastic strain reaches a critical value. A crack initiating from the node where a failure first occurs is taken to propagate to the adjacent node that has the highest value of the failure parameter (the maximum tensile principal stress or the effective plastic strain). The opening and propagation of a crack are modeled by the node release technique. Surface tractions and the normal component of the heat flux are taken to be null on the newly created crack surfaces. For the brittle failure, the stress field around the crack tip resembles that in mode-I deformations of a prenotched plate loaded in tension. The distribution of the effective plastic strain in a small region around the surface of the notch-tip is not affected much by the initiation of a ductile fracture there except for a shift in the location of the point where the effective plastic strain is maximum. The initiation of the ductile failure is delayed when a crack is opened at the point where the brittle failure ensues.     

Effect of bending moment on the dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. As an extension of previous work, an induced bending moment generated during fracture is incorporated into the analysis and this improved formulation is presented. The crack length, crack tip speed, axial force and bending moment on the fracturing section are determined as functions of time after crack initiation. It is found that the bending moment has a significant effect on the fracture process in that it tends to retard fracture and causes a drastic change in the slope of the loading curve for large crack depths. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate in pure tensile loading.     

Plastic yielding at the tip of a blunt notch during static and fatigue loading

Rice's analytical Mode III solution for the relationship between anti-plane stress and anti-plane strain was used to determine the small scale plastic yielding at the tip of a two-dimensional blunt notch. The results were applied to fatigue loading. The plastic zone size and crack opening displacement derived in the present analysis were determined as functions of applied stress, geometric factors (notch radius and length) and material properties (yield stress and the work hardening rate). The minimum stress intensity required for plastic yielding at a blunt notch tip was postulated to be the experimentally observed threshold stress intensity for fatigue crack initiation. The threshold stress intensity so determined depends not only on the notch geometry but also on material properties. There is good agreement with calculated and measured values of the threshold stress intensity for fatigue crack initiation.     

单边切口薄板研究聚乙烯醇纤维增强水泥基复合材料断裂韧性

利用单边切口薄板对配制的聚乙烯醇纤维增强水泥基复合材料进行单轴直接拉伸试验研究,得到硬化的荷载-裂缝张开位移全曲线。通过试验观察到缺口尖端处出现呈发散状的多条微小裂纹,部分试件在远离切口处还有多条裂缝出现,并不像混凝土或水泥净浆这类半脆性、脆性材料只有单条裂缝并沿着单条路径开裂,因此,适用于应变软化材料的双K断裂理论以及断裂能理论不能直接用在应变已经发生假硬化的材料中。鉴于上述原因,该文提出起裂断裂韧度和耗散能两个韧性评价指标。     

Effect of shear and rotary inertia on dynamic fracture of a beam or plate in tensile loading

The dynamic fracture response of a long beam of brittle material subjected to tensile loading is studied. If the magnitude of the applied tensile loading is increased to a critical value, a crack will propagate from one of the longitudinal surfaces of the beam. As an extension of previous work, the effect of shear and of rotary inertia on the tensile loading and the induced bending moment at the fracturing section is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment and axial force at the fracture section are determined as functions of time after crack initiation. It is found that the rotary effect diminishes the bending moment effect and retards total fracture time whereas the shear has an opposite effect. Thus by combining the two effects (to simulate to first order the Timoshenko beam) overall fracture is retarded. The results also apply for plane strain fracture of a plate in tensile loading provided the value of the elastic modulus is appropriately modified.     

A Fracture Probability Competition Mechanism of Stress Corrosion Cracking

The stress corrosion cracking (SCC) of austenitic stainless steel was studied via polarization, slow strain rate and scanning electron microscope (SEM) techniques. Many SCC mechanisms have been proposed in which hydrogen embrittlement and passive film rupture-repassivation theories are generally accepted, but they can hardly explain the SCC mechanism of austenitic stainless steel in acidic chloride solution adequately, because the steel is in active dissolution state and cathodic polarization can prevent it from occurring. Our experiment shows that the anodic current increases the creep rate and decreases the plastic strength of the material on single smooth specimen as well as at the SCC crack tip. The fractured surface was characterized as brittle cleavage, while the surface crack of smooth specimen was almost vertical to the tensile strength, which can confirm that the cracks were caused by tensile stresses. A fracture probability competition mechanism of SCC was proposed on the basis of the experimental results combined with the viewpoint of ductile-brittle fracture competition. When the anodic dissolution current is increased to a certain degree, the probability of fracture by tensile stress will exceed that by shear stress, and the brittle fracture will occur. The proposed SCC mechanism can riot only explain the-propagation of SCC cracks but can explain the crack initiation as well. The strain on the surface distributes unevenly when a smooth specimen is deformed, so does the anodic current distribution. The crack will initiate at a point where the anodic current density is large enough to cause the material at a specific point to fracture in brittle manner.     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

Dynamic asymptotic mode III crack tip field in rate dependent materials

The asymptotic field at a dynamically growing crack tip in strain-rate sensitive elastic-plastic materials is investigated under anti-plane shear loading conditions. In the conventional viscoplasticity theory, the rate sensitivity is included only in the flow stress. However, it is often found that the yield strength is also affected by previous strain rates. The strain rate history effects in metallic solids are observed in strain rate change tests in which the flow stress decreases gradually after a rapid drop in strain rate. This material behavior may be explained by introducing the rate sensitivity in the hardening rule in addition to the flow rule. The strain-rate history effect is pronounced near the propagating crack where the change of strain rates take place. Effects of the rate dependency in the flow rule and the hardening rule on the crack propagation are analyzed. The order of the stress singularity in the asymptotic field is determined in terms of material parameters which characterize the rate sensitivity of the material. The results show that an elastic sector is present in the wake zone when the rate-dependency is considered only in the hardening rule. Terminal crack propagation speed is determined by applying the critical stress fracture criterion and the critical strain criterion to the asymptotic fields under the small scale yielding condition.     

Thickness effect on crack tip deformation at fracture

The crack tip deformation at the onset of surface crack growth for four single edge cracked specimens having four different thicknesses were studied. The specimens were made of the ductile and tough HY-80 steel. The thickness contraction in the crack tip region and the tensile strain in the direction of load were measured. The crack tip necking-in acts like a notch. The depths, the root radii, and the angle changes of the necking-in notches were measured. The results indicated that the near tip strain can be used as a fracture criterion of ductile and tough materials. It was also found that the fracture strengths of the cracked specimens can be correlated with the tensile ductilities measured with Clausing specimens.     

Analytical study of the elastic–plastic stress fields ahead of parabolic notches under antiplane shear loading

An analytical study is carried out on the elastic–plastic stress and strain distributions and on the shape of the plastic zone ahead of parabolic notches under antiplane shear loading and small scale yielding. The material is thought of as obeying an elastic-perfectly-plastic or a strain hardening law. When the notch root radius becomes zero, the analytical frame matches the solutions for the crack case due to Hult–McClintock (elastic-perfectly-plastic material) and Rice (strain hardening material). The analytical frame provides an explicit link between the plastic stress and the elastic stress at the notch tip. Neuber’solution for blunt notches under antiplane shear is also obtained and the conditions under which such a solution is valid are discussed in detail by using elastic and plastic notch stress intensity factors. Finally, revisiting Glinka and Molski’s equivalent strain energy density (ESED), these factors are used also to give, under antiplane shear loading, the increment of the strain energy at the notch tip with respect to the linear elastic case.     

Micromechanics of Fiber‐Reinforced Cementitious Composites

The strain hardening and tension softening response of short fiber‐reinforced cementitious composites under unidirectional tensile/flexural loading is modelled using concepts from fracture and damage mechanics. The tensile strain hardening in these composites is due to the formation of microcracks which are however prevented from coalescing by the bridging action of the fibers. The density of microcracks increases with increasing tensile/flexural loading until it reaches a saturation level at the tensile load carrying capacity of the composite. Thereafter the fibers progressively debond from the elastic matrix and the deformation begins to localise in the eventual fracture plane, first as unconnected cracks and later as a connected through crack subjected to the residual frictional bridging action by the fibers.     

Adiabatic shear banding in a thick-walled steel tube

We analyze the initiation and propagation of adiabatic shear bands in a thick-walled 4340 steel tube with a V-notch in the middle. The material is modeled as strain hardening, strain-rate hardening and thermal softening. The deformations are assumed to be locally adiabatic and the effect of inertia forces is considered. Two different loadings, i.e., torsional, and combined torsional and axial pressure are considered. In each case, the load generally increases linearly from zero to the final value, is kept steady there for some time, then decreases to zero and is kept at zero; thus a finite amount of energy is input into the body. For the combined loading, the magnitude of the torsional loading pulse is kept fixed and the effect of varying the magnitude of the axial pressure preload is investigated. A shear band first initiates in the element adjoining the notch tip and propagates radially inwards. By recording the time when a shear band initiates at the centroids of different elements we determine its speed of propagation in the radial direction to vary from approximately 50 m/s at the instant of its initiation in an element abutting the notch tip, to nearly 90 m/s by the time it reaches the innermost surface of the tube; the speed also depends upon the overall loading rate, and whether or not the loading is multiaxial. The drop in the torque required to twist the tube at the initiation of a shear band is not as sharp as that in a thin-walled steel tube. We compute the distance through which a shear band propagates as a function of the energy input into the body and thus ascertain the energy required to drive a shear band through a unit distance. We also study torsional deformations of a thick-walled CR-300 steel tube, model its thermal softening by a relation proposed by Zhou et al. and use material properties derived from their data. In this case, the speed of a shear band initiating from an element abutting the notch tip is found to vary between 750 m/s and 1,000 m/s at different points on a radial line through the notch tip; this agrees with that observed by Zhou et al. in their experiments on single-notched plates.     

The cohesive crack concept: application to PMMA at −60 °C

This paper provides a large number of experimental results from the fracture of round-notched samples of a material that remains essentially in the linear elastic regime up to crack initiation. Loading of the samples ranged from pure tensile up to bending. Notch acuity was changed by changing the notch tip radii, notch angle and notch depth. All these experimental results have been used to analyze the predictive capability of the cohesive crack model. All tests were numerically simulated and several criteria justifying the adopted softening function are discussed. The agreement between numerical prediction and experimental results was very good.