Influence of stress triaxiality on damage and crack tip opening displacement parameters for steels

The dependence of the void growth parameter on the local stress triaxiality and local effective plastic strain near the crack tip of ductile materials provides the motivation to seek for parameters that could rank the ductility of steels. Experimental data for AS 1405-180, AS 1204-350, HY-80 and C---Mn steels show that the crack tip opening displacement (CTOD) at initiation δ_c decreases with increasing crack tip stress triaxiality. This trend is confirmed by analysis. As the critical local effective plastic strain ε_ec also decreases with increasing local stress triaxiality, the ratio δ_c/ε_ec is found to remain nearly constant or independent of the local constraint, i.e., the stress triaxiality. These parameters are given for a class of steels in this paper. Their association with the resistance to ductile fracture remains to be investigated.     

An analysis of ductile rupture in notched bars

Ductile fracture in axisymmetric and plane strain notched tensile specimens is analyzed numerically, based on a set of elastic-plastic constitutive relations that account for the nucleation and growth of microvoids. Final material failure by void coalescence is incorporated into the constitutive model via the dependence of the yield function on the void volume fraction. In the analyses the material has no voids initially; but as the voids nucleate and grow, the resultant dilatancy and pressure sensitivity of the macroscopic plastic flow influence the solution significantly. Considering both a blunt notch geometry and a sharp notch geometry in the computations permits a study of the relative roles of high strain and high triaxiality on failure. Comparison is made with published experimental results for notched tensile specimens of high-strength steels. All axisymmetric specimens analyzed fail at the center of the notched section, whereas failure initiation at the surface is found in plane strain specimens with sharp notches, in agreement with the experiments. The results for different specimens are used to investigate the circumstances under which fracture initiation can be represented by a single failure locus in a plot of stress triaxiality vs effective plastic strain.     

考虑应力三轴度影响的30CrMnSiNi2A钢韧性断裂研究

30CrMnSiNi2A钢是一种在军工领域应用广泛的低合金高强度钢。针对结构完整性的评估问题,采用试验和数值计算结合的方法研究了30CrMnSiNi2A钢的韧性断裂特性。对光滑圆棒试件在不同温度下进行准静态和动态拉伸试验,并通过有限元迭代方法标定了材料的Johnson-Cook动态本构模型参数,分析了温度和应变率对30CrMnSiNi2A钢断裂行为的影响。开展了缺口圆棒拉伸、缺口平板剪切和圆柱压缩试验,计算了各试件对应的平均应力三轴度和断裂应变,给出了应力三轴度在?1/3～1.5区间内的断裂应变变化曲线,分别确定了Johnson-Cook和Bao-Wierzbicki失效模型参数。研究表明,30CrMnSiNi2A钢的断裂应变与应力状态密切相关,且在不同的应力三轴度区间内曲线单调性差异较大,Bao-Wierzbicki失效模型较好地描述了这种钢在不同应力状态下的断裂特性。     

Damage characterization of SAE 1020 and 1045 steel under torsion and compression

A damage model is applied to characterize the ductile deformation of SAE 1020 and 1045 steel. Damage is evaluated for thin-walled cylindrical specimens in torsion and solid bar specimens in compression where stress triaxiality enhances crack initiation. Analyzed are the variations of the damage parameter with the average compressive axial strain at the different locations of the solid bar. Initially, stress triaxiality being largest at the center appeared to dominate damage. With increasing strain, pronounced damage tends to occur in the mid-plane at locations closer to the free surface. Change in the aspect ratio of the cylindrical bar specimens also had an effect on the stress triaxiality and hence the damage parameter. Less damage is prediated for slender bars at the same strain level although the difference is small for height to diameter ratio up to 1.86.     

Predicting ductile fracture of low carbon steel sheets: Stress-based versus mixed stress/strain-based Mohr–Coulomb model

Two distinct implementations of the Mohr–Coulomb failure model are used in conjunction with a non-associated quadratic plasticity model to describe the onset of fracture in low carbon steel sheets. The stress-based version corresponds to the original Mohr–Coulomb model in stress space. For the mixed stress/strain-based version, the Mohr–Coulomb failure criterion is first transformed into the space of stress triaxiality, Lode angle parameter and equivalent plastic strain and then used as stress-state dependent weighting function in a damage indicator model. Basic fracture experiments including tensile specimens of different notch radii and a punch test are performed to calibrate the material parameters of the respective models. Subsequently, the models are used to predict the crack initiation in a Hasek test and during the stamping of an anticlastic structure. Unlike for the calibration experiments, the loading history during stamping is highly non-linear. Both models can be calibrated with similar accuracy, but the strain-based model predicts the instant of onset of fracture with greater accuracy in the stamping experiment which is an advantage of the empirical damage accumulation rule.     

高强钢广义屈服和破坏理论

结合经典强度理论和现代损伤力学对金属屈服和断裂解释的力学原理,给出了高强钢在应力三轴空间广义屈服轨迹方程的新诠释.根据三向等拉伸应力状态下高强钢屈服和宏观脆断的重合性,提出了高强钢在应力三轴空间的开裂准则.通过对高强钢刻痕杆断裂试验的数值模拟分析,对比验证了该开裂准则的普适性及精度.最后,给出了高强钢广义强度理论的物理解释及抗断设防.建议的广义强度理论是解高强钢裂纹体和无裂体断裂的一个尝试.     

准静态条件下金属材料的临界断裂准则研究

本文针对9种金属材料完成了具有不同约束程度的10类试样的延性断裂试验, 获得了发生拉、压、扭和裂尖断裂等破坏形式构型试样的载荷-位移试验关系; 基于圆棒漏斗试样拉伸试验所得直至破坏的载荷-位移曲线, 采用有限元辅助试验(finite-element-analysis aided testing, FAT)方法得到了9种材料直至破坏的全程等效应力-应变曲线, 以此作为材料本构关系通过有限元分析获得了各类试样直至临界破坏的载荷-位移关系模拟. 载荷-位移关系模拟结果与试验结果有较好的一致性, 表明用于解决试样颈缩问题的FAT方法所获得的全程材料本构关系针对各向同性材料具有真实性和普适性. 对应9种材料、10类试样的36 个载荷-位移临界断裂点, 通过有限元分析获得了对应的材料临界断裂应力、应变与临界应力三轴度, 研究表明, 第一主应力在延性变形过程中为主控断裂的主导参量; 通过研究光滑、缺口、裂纹等构型试样的断裂状态, 提出了$-1$至3范围的应力三轴度下由第一主应力主控的统一塑性临界断裂准则.      

Plasticity and fracture of martensitic boron steel under plane stress conditions

Two series of multiaxial experiments are performed to characterize the mechanical behavior of a hot formed martensitic 22MnB5 boron steel. In the first series, flat specimens of uniform cross-section are subjected to various combinations of tensile and shear loading to characterize the elasto-plastic response. Butterfly-shaped specimens of non-uniform cross-section are used for the second series to study the onset of fracture in the martensitic steel. It is found from the analysis of the experimental results that the planar isotropic Hill’48 yield function along with an associated flow rule provides good estimates of the stress–strain response over a wide range of loading paths. The fracture experiments demonstrate that the crack initiation depends strongly on the loading state. A simple stress triaxiality dependent phenomenological fracture model is calibrated to describe the onset of fracture. Using the proposed plasticity and fracture model, numerical simulations of the fracture of tensile specimens of different notch radii are performed and compared with experiments.     

应力三轴度的有限元计算修正

对某高强度钢制成的光滑圆棒和缺口圆棒进行了系列准静态拉伸实验,采用ABAQUS对每个试 件进行了数值模拟,得到了该材料的真实应力应变曲线,拟合出了J-C本构模型和失效模型的部分材料常数。 最后,对该高强度钢制成的平板进行了撞击实验,并用得到的J-C模型对平板撞击实验进行了数值模拟,计算 结果与实验结果吻合很好,证明利用数值模拟并修正应力三轴度的方法是可行的。     

Tension–torsion fracture experiments – Part II: Simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain

An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing.     

Fracture of composite laminates by three-point bend

An experimental investigation has been carried out on the fracture behavior of T300/5208 graphite/epoxy laminates using three-point bend and tension tests. One laminate, a [0/±45/90] _ns orientation, was used withn=1 for tension specimens andn=4 and 8 for bend specimens. The crack-growth-resistance curve was constructed by compliance matching from crack-opening displacement and load data obtained from three-point bend tests. The value of effective crack length and corresponding crack resistance at onset of instability was nearly constant and independent of the initial crack length and laminate thickness. Experimental data from both bend and tension tests correlated reasonably well to the average-stress-failure criterion. Data were also compared with results found in the literature.     

含缺口试件疲劳全寿命预测一种建议的方法

传统的研究含缺口构件的疲劳的方法是将疲劳启裂和疲劳裂纹扩展两个过程完全独立起来,用不同的方法来模拟,相互间并没有定量的关系。本文是基于最新发展的多轴疲劳损伤理论,建立了一种适用于各种载荷条件下的疲劳启裂和裂纹扩展的普适方法。根据从弹塑性分析中得到的应力应变,确定疲劳损伤模型,建立能够预测疲劳启裂、裂纹扩展速率和扩展方向的新方法。整个模拟可以分为两步:弹-塑性应力分析得到材料的应力应变分布;再运用一个通用的疲劳准则预测疲劳裂纹启裂和裂纹扩展。通过对1070号钢含缺口试件的疲劳全寿命预测,得到了与实验非常吻合的模拟结果。     

6061-T6铝合金动态拉伸本构关系及失效行为

采用HMH-206高速材料试验机开展了6061-T6铝合金在0.001～100 s-1应变率范围内的静、动态拉伸力学性能实验,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对6061-T6铝合金流动应力和应变率敏感性指数的影响,并基于实验结果对Johnson-Cook本构模型进行了修正。结合缺口试件的实验结果和模拟数据,得到了材料的Johnson-Cook失效模型参数,并对模型的准确性和适用性进行了验证。结果表明,在拉伸载荷作用下,6061-T6铝合金表现出明显的应变硬化特征和应变率敏感性,其流动应力随应变率的升高而提高,修正的Johnson-Cook本构模型可以描述材料的动态塑性流动行为,建立的Johnson-Cook失效模型能够表征材料的断裂失效行为。     

16MnR钢缺口试样解理断裂行为研究

研究了低合金热轧钢16MnR缺口试样在$-196\,{^\circ}$C和$-130\,{^\circ}$C的解理断裂机 理. 拉伸试验、单、双缺口四点弯曲实验、断口形貌观察以及有限元分析结果表明, 缺口试 样发生解理断裂时均起裂于夹杂物粒子, 一种位于缺口根部前端(IC型), 另一种位于距缺口 根部较远的条形裂纹前端(SIC型); 且随温度升高, 起裂源的类型从$-196\,{^\circ}$C下的IC 型转变为$-130\,{^\circ}$C下的SIC型. 微裂纹均形核于夹杂物, 最终的断裂由铁素体晶粒尺 寸的微裂纹扩展控制. 缺口试样IC型解理断裂遵循裂纹形核条 件$\varepsilon_{\rm p} \ge \varepsilon_{\rm pc}$和裂纹扩展条件$\sigma_{yy} \ge \sigma_{f}$, 而SIC型解理断裂条件则演化为$\varepsilon_{\rm p}+\varepsilon_{\rm ps} \ge \varepsilon_{\rm pc}$和$\sigma_{yy} +\sigma_{yy{\rm s}} \ge \sigma_{f}$.     

基于应力三轴度和罗德参数的6061和7075铝合金材料断裂失效分析

分别对6061铝合金和7075铝合金材料的缺口圆棒试件和凹槽平板试件进行准静态拉伸试验,并采用ABAQUS软件对拉伸过程进行数值模拟。模拟结果与试验测试结果吻合很好,验证了有限元模型的合理性和可靠性。通过有限元模拟,分别给出了不同试件的应力三轴度和罗德参数随等效塑性应变的变化曲线以及两种材料的失效轨迹,并对它们进行了分析讨论。结果表明:形状相同、材料性质不同的试件,应力三轴度的演化规律不同;材料的失效应变受应力三轴度和罗德参数的影响,并且不同性质的材料对罗德参数的敏感性不同。     

Determination of the material fracture toughness by numerical analysis of 3D elastoplastic dynamic deformation

We develop a technique for calculating the plastic strain and fracture toughness fields of a material by solving dynamical 3D problems of determining the stress-strain state in the elastoplastic statement with possible unloading of the material taken into account. The numerical solution was obtained by a finite difference scheme applied to the three-point shock bending tests of parallelepiped-shaped bars made of different materials with plane crack-notches in the middle. The fracture toughness coefficient was determined for reactor steel. The numerically calculated stress tensor components, mean stresses, the Odquist parameter characterizing the accumulated plastic strain, and the fracture toughness are illustrated by graphs.     

Simulation of failure under cyclic plastic loading by damage models

The purpose of this work is to simulate the evolution of ductile damage and failure involved by plastic strain reversals using damage models based on either continuum damage mechanics (CDM) or porosity evolution. A low alloy steel for pressure vessels (20MnMoNi55) was chosen as reference material. The work includes both experimental and simulation phases. The experimental campaign involves different kinds of specimens and testing conditions. First, monotonic tensile tests have been performed in order to evaluate tensile and ductile damage behaviour. Then, the cyclic yielding behaviour has been characterized performing cyclic plasticity tests on cylindrical bars. Finally, cyclic loading tests in the plastic regime have been made on different round notched bars (RNBs) to study the evolution of plastic deformation and damage under multiaxial stress conditions. The predictions of the different models were compared in terms of both, the specimens macroscopic response and local damage. Special emphasis was laid on predictions of the number of cycles prior to final failure and the crack initiation loci.     

Correlation of notch bar, metal overturn and forming data involving effective plastic strain and stress triaxiality ratio

Starting with a macrodamage parameter that relates the effective plastic strain and exponential function of stress triaxiality, a simple expression is obtained that is reminiscent of those used by other in void growth prediction. Good correlations are obtained for data on notched circular bar and sheet metal forming in addition to the problem where the triaxial stress state reversed sign. The results are affected by the fabrication condition. What has been provided is a simple means of ranking the workability of metal products that undergo plastic deformation. Limits are established in accordance with the onset of macrocracking.     

Fracture Characterization of Steels by Means of the Small Punch Test

A hot rolled API X-70 steel plate and its heat-affected zone (the region with the maximum hardness and lowest toughness of the welded joint made using this steel) were employed to obtain the material’s room temperature elasto-plastic fracture toughness, J_Ic, by means of small punch tests (SPTs) using both conventional un-notched samples and longitudinally-notched SPT specimens. In the latter case, the notches were manufactured by micromachining different notch depth-to-thickness ratios (a/t?=?0.3 and 0.4). The representative toughness parameter used with the conventional SPT tests was the maximum strain measured directly in the failed region, while in the case of the notched samples, the consumed energy until the initiation of a crack from the tip of the notch was considered the most useful parameter of choice. The onset of crack initiation was determined directly from the load-displacement plot of each test with the aid of scanning electron microscope observations performed on different samples over which interrupted tests had been conducted. These tests were interrupted at different percentages of the maximum registered load. A simple correlation between the energy consumed until the initiation of crack growth in the notched SPT sample and the critical J value obtained using standard tests (J-R curves) was determined, defining an easy and promising way to derive fracture toughness from miniature SPT tests.     

On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part I. Experiments

Notched axisymmetric specimens of the structural steel Weldox 460 E have been tested at high strain rates in a Split Hopkinson Tension Bar. The aim was to study the combined effects of strain rate and stress triaxiality on the material's behaviour. It is further considered important to obtain experimental data that can be used in validation of constitutive relations and fracture criteria. The force and elongation of the specimens were measured by strain gauges during the high strain rate tests, while the fracture strain was calculated based on measurements of the fracture area in the microscope. Optical recordings of the notch deformation were obtained using a digital high-speed camera system. Using image processing of the digital images, it was possible to estimate the true strain against time at minimum cross-section. The strength of the material was found to increase with increasing strain rate, while for the ductility no significant effect of strain rate could be ascertained from the notched specimen tests. The ductility of the material was found to depend considerably on the stress triaxiality.