Effects of the stress state on plastic deformation and ductile failure: Experiment and numerical simulation using a newly designed tension‐shear specimen

The stress state is one of the most notable factors that dominates the initiation of ductile fracture. To examine the effects of the stress state on plasticity and ductile failure, a new tension‐shear specimen that can cover a wide range of stress triaxialities was designed. A fracture locus was constructed in the space of ductility and stress triaxiality for two typical steels based on a series of tests. It is observed that the equivalent plastic strain at failure exhibits a nonmonotonic variation with increasing the value of stress triaxiality. A simple damage model based on the ductility exhaustion concept was used to simulate the failure behaviour, and a good agreement is achieved between simulation results and experimental data. It is further shown that consideration of fracture locus covering a wide range of stress triaxialities is a key to an accurate prediction.     

Investigation on fracture mechanisms of metals under various stress states

Fracture mechanisms for widely used metal materials are investigated under various loading conditions. Several specimens and different loading methods are deliberately designed to produce various stress states. The stress triaxiality is used to rate the level of tension and compression under various stress states. The stress triaxiality increases with adding a notch in the specimen under tension loading and decreases by changing the loading from tension to compression. Scanning electron microscopes are used to observe the microscopic features on the fracture surfaces. The fracture surfaces observed in the tests indicate that with the decreasing stress triaxiality the fracture mechanism for a given metal material includes intergranular cleavage, nucleation, growth, void coalescence, and local shear band expansion. With the fracture mechanisms changing from intergranular cleavage to nucleation, growth, and coalescence of voids, and expansion of a local shear band, four possible fracture modes can be observed, which are quasi-cleavage brittle fracture, normal fracture with void, shear fracture with void, and shear fracture without void. Quasi-cleavage brittle fracture and normal fracture with void are both normal stress-dominated fracture modes; however, their mechanisms are different. Shear fracture with and without void are both shear stress-dominated fracture, and shear fracture with void is also influenced by the normal stress. To a certain metal material, under high stress triaxiality, quasi-cleavage brittle fracture and normal fracture with void tend to occur, and under low stress triaxiality, shear fracture with and without void tend to occur. In addition, the critical positions and fracture criteria adapted to each fracture mode will also be different.     

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension (a/W=0.5) and three-point bend (a/W=0.1 and 0.5) specimens under plane stress condition. The crack growth is controlled by the experimental J-integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack- tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dependence of ductile crack formation in tensile tests on stress triaxiality, stress and strain ratios

An experimental and numerical study on ductile crack formation in tensile tests was conducted. Five different specimens including flat specimens, smooth round bars, notched bars (two types) and flat-grooved plates were investigated. Von Mises equivalent strain to crack formation, stress triaxiality, and stress and strain ratios at critical locations, were obtained. Accuracy of the Bridgman formulas for stresses in necked round bars, and McClintock's model for flat-grooved plates, were studied. A relationship between the stress triaxiality and equivalent strain to crack formation was determined in a high stress triaxiality range for Al 2024-T351. More importantly, it was found that equivalent strain and stress triaxiality are the two most important factors governing crack formation, while stress and strain ratios cause secondary effects. It appears possible to make a good prediction of crack formation with equivalent strain and stress triaxiality.     

Development of stress-modified fracture strain for ductile failure of API X65 steel

The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

Unified triaxiality at the crack tip subjected to plane strain condition under mixed‐mode (I + II) fracture

The new model of stress triaxiality, subjected to plane strain condition under mixed‐mode (I + II) loading, at the yield loci of the crack tip, has been formulated using unified strength theory. It evaluates critical values of triaxiality for various convex and non‐convex failure criteria, unlike the existing model. It shows the effects of Poisson's ratio and intermediate principal stress for materials whose strength in tension and compression is either equal or unequal. Further, on this basis, the crack initiation angles are predicted for various crack inclinations and compared with those obtained from other fracture criteria. The plastic zone shapes supplement the results. Critical yield stress factor, a significant parameter at the crack tip got lowered as the difference among the three principal stresses reduced to a minimum. The crack initiation angles obtained from the model showed good agreement with those obtained from G‐, S‐, and T‐criterion.     

Fracture and yield behavior of adhesively bonded joints under triaxial stress conditions

Most of adhesively bonded joints are under complicatedly distributed triaxial stress in the adhesive layer. For the estimating of the strength of adhesively bonded joints, it is crucial to clarify behavior of yield and failure of the adhesives layer under triaxial stress conditions. Two types of the adhesively bonded joints were used in this study: One is the scarf joint which is under considerably uniform normal and shear stresses in the adhesive layer, where their combination ratio can be varied with scarf angle. The other is the butt joint with thin wall tube in which considerably uniform pure shear can be realized in the adhesive layer under torsional load conditions. These joints can cover the stress triaxiality in adhesive layers of most joints in industrial application. The effect of stress triaxiality on the yield and fracture stresses in the adhesive layer were investigated using the joints bonded by three kinds of adhesives in heterogeneous and homogeneous systems. The results showed that both the yield and failure criterion depend on the stress triaxiality and that the fracture mechanism of the homogeneous adhesive is different from that of the heterogeneous one. From these experimental results, a method of estimating the yield and failure stresses was proposed in terms of a stress triaxiality parameter.     

Investigation of fracture mechanism of 6063 aluminum alloy under different stress states

Fracture mechanisms in a 6063 aluminum alloy were investigated and analyzed carefully by in-situ tensile tests in SEM with a vacuum chamber. Specimens used were designed to produce different stress states. Studies indicated that with stress triaxiality (σ _m/σ _e) decreasing, the fracture modes changed from normal fracture to shear fracture and the fracture surfaces changed from the dimples and intragranular dominated fracture mode to the shear dominated fracture mode. The grain boundaries of the 6063 aluminum alloy were the weakest positions. In the case of high stress triaxiality, the grain boundary cracks were produced by normal stress or by the incompatibility of deformation between neighboring grains, and the normal stress dominated the crack propagation. In the case of low stress triaxiality, the boundary cracks were produced by the relative slipping of grains against neighboring grains, and the shear stress dominated the crack propagation. The final fracture of the specimens occurred by connections of cracks through transgranular cracking of the ligaments among these cracks.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

一种韧性断裂模型的理论研究和实验验证

为研究高强钢板成形过程中的损伤破裂机理,更准确地预测高强钢的断裂失效行为,基于细观损伤力学的空穴理论,并在屈服函数就是塑性势函数的通用性假设基础上推导了各向同性的韧性断裂模型;同时引入Lode参数以反映不同应变状态下空穴形核、长大以及聚合的差异,提出了一种包含应力三轴度和Lode参数的新模型.在Hill正交各向异性屈服假设下,描述了平面应力状态下应力比值、r值与应力三轴度、等效塑性应变的关系.最后,针对DP590进行了参数确定和实验验证.结果表明:应力三轴度在高强钢韧性断裂中仍然起主导因素,在低应力三轴下,材料主要是剪切型破坏,空穴的长大及聚合方式主要受剪应力影响,高应力三轴下,空穴损伤主要受拉应力影响,断裂是韧窝形的;Lode参数决定了应力组成形式,也间接地反映了应变状态,它与应力三轴度共同决定了空穴损伤的发展.新的模型能较准确地预测DP590的成形极限.     

Comparison of cohesive zone parameters and crack tip stress states between two different specimen types

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality.     

考虑罗德角参数的钢材薄板延性断裂标定方法

在钢结构中钢梁腹板的断裂表现出很强的剪切断裂特征,因此在预测其断裂行为时除了考虑应力三轴度以外,还应考虑与剪切状态有关的罗德角参数的影响。该文提出了一种适用于钢材薄板延性断裂预测的标定方法。共设计了5组试件,分别为平板试件、开孔平板、开槽平板、90°剪切平板和45°剪切平板。利用平板试件和停机平板试件单向拉伸试验,结合有限元反演得到钢材的全过程真实应力-应变曲线。然后将其代入各试件有限元模型进行计算,标定出各试件对应的等效断裂应变、平均应力三轴度和平均罗德角参数。最后利用Matlab优化工具箱对断裂模型进行优化拟合,确定模型中的各项待定参数。     

On the influence of state of stress on ductile failure initiation in high strength steels

The effect of stress state on the effective plastic strain to initiate ductile failure in three high strength steels is investigated. Circumferentially notched tension specimens were used, and failure initiation strains were correlated with a parameter which is a measure of the “triaxiality” of the stress state. Results are given for both in-plane and through-thickness directions in rolled plate.The failure initiation data, together with appropriate stress-strain fields, and estimates of characteristic lengths over which failure initiates, have been used to predict failure initiation at notches and at crack tips; conventional fracture mechanics parameters, such as K_I at crack extension in small scale yielding are estimated for one of the high strength steels.     

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.     

Influence of Triaxial Stress State on Ductile Fracture Strength of Polycrystalline Nickel

In this contribution, the effect associated with stress triaxiality on ductile damage evolution in high purity nickel has been investigated from both experimental and theoretical points of view. Tensile tests on smooth and notched round bar specimens were performed to calibrate the fracture strain in a wide range of stress triaxiality. The capability of the Gurson model to reproduce and predict physical failure behaviour was examined. It was shown that stress triaxiality played a major role on damage evolution as demonstrated by the progressive reduction of material ductility under increasing triaxial states of stress.     

Fracture mechanisms of aluminium alloy AA7075-T651 under various loading conditions

The fracture behaviour of the aluminium alloy AA7075-T651 is investigated for quasi-static and dynamic loading conditions and different stress states. The fracture surfaces obtained in tensile tests on smooth and notched axisymmetric specimens and compression tests on cylindrical specimens are compared to the fracture surfaces that occur when a projectile, having either a blunt or an ogival nose shape, strikes a 20 mm thick plate of the aluminium alloy. The stress state in the impact tests is much more complex and the strain rate significantly higher than in the tensile and compression tests. Optical and scanning electron microscopes are used in the investigation. The fracture surface obtained in tests with smooth axisymmetric specimens indicates that the crack growth is partly intergranular along the grain boundaries or precipitation free zones and partly transgranular by void formation around fine and coarse intermetallic particles. When the stress triaxiality is increased through the introduction of a notch in the tensile specimen, delamination along the grain boundaries in the rolling plane is observed perpendicular to the primary crack. In through-thickness compression tests, the crack propagates within an intense shear band that has orientation about 45° with respect to the load axis. The primary failure modes of the target plate during impact were adiabatic shear banding when struck by a blunt projectile and ductile hole-enlargement when struck by an ogival projectile. Delamination and fragmentation of the plates occurred for both loading cases, but was stronger for the ogival projectile. The delamination in the rolling plane was attributed to intergranular fracture caused by tensile stresses occurring during the penetration event.     

ANALYSIS OF CAST STEEL FRACTURE MECHANISMS FOR DIFFERENT STATES OF STRESS

The process of fracture in a low-carbon cast steel was studied for different states of stress. As a result of heat treatment, two different microstructures have been obtained: ferritic-pearlitic and bainitic. The triaxial states of stress were realised by tensile tests on specimens with various notch configurations and on smooth specimens subjected to different hydrostatic pressures.
During tensile tests carried out under triaxial stress states, the following quantities at fracture were determined: the effective strain, effective stress, stress state components, mean stress and stress triaxiality factor. Fractography of the specimens was carried out to observe the fracture mechanisms and relate them to the state of stress. The fracture mechanism depended on the state of stress and microstructure. With a decreasing stress triaxiality factor, the failure mechanism changed from ductile to shear. The fracture mechanism changed across the diameter of the sample and also depended on the microstructure. The small, smooth samples fractured at a higher stress than the larger samples. Ductile fracture in the ferritic-pearlitic microstructure was controlled by cracking of the matrix–precipitate boundary. Samples with the bainitic microstructure fractured by shear, and fracture depended mainly on the effective stress, although void growth (which is controlled by stress triaxiality) reduced the critical effective stress at positive values of mean stress.     

A STUDY ON FATIGUE CRACK GROWTH UNDER OUT-OF-PHASE COMBINED LOADINGS

Abstract— Fatigue tests were performed on thin-walled tubular specimens of S45C steel under tension-compression, pure torsion, in-phase and out-of-phase axial-torsional loadings. The relationship between cracking behaviour and stress components on the crack plane was investigated. Measurement of microcrack density showed that microcracking was governed predominantly by the shear stress amplitude acting on the crack plane for all loading conditions. The failure crack was formed by coalescence of many cracks initiated near the maximum shear planes. The cracks grew turning their orientation to the direction perpendicular to the maximum normal stress. The transition of crack orientation occurred at relatively longer crack lengths at a higher stress ratio. The crack growth behaviour for all loading modes can be correlated using an equivalent strain intensity parameter based on shear and normal strains on the crack plane.     

Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading

The present paper is concerned with multi-axial ductile fracture experiments on sheet metals. Different stress-states are achieved within a flat specimen by applying different combinations of normal and transverse loads to the specimen boundaries. The specimen geometry is optimized such that fracture initiates remote from the free specimen boundaries. Fracture experiments are carried out on TRIP780 steel for four different loading conditions, varying from pure shear to transverse plane strain tension. Hybrid experimental–numerical analyses are performed to determine the stress and strain fields within the specimen gage section. The results show that strain localization cannot be avoided prior to the onset of fracture. Through-thickness necking prevails under tension-dominated loading while the deformation localizes along a band crossing the entire gage section under shear-dominated loading. Both experimental and simulation results demonstrate that the proposed fracture testing method is very sensitive to imperfections in the specimen machining. The loading paths to fracture are determined in terms of stress triaxiality, Lode angle parameter and equivalent plastic strain. The experimental data indicates that the relationship between the stress triaxiality and the equivalent plastic strain at the onset of ductile fracture is not unique.