Fracture prediction in stretch forming using finite element simulation combined with ductile fracture criterion

Summary  A criterion for ductile fracture is introduced in the finite element simulation of sheet metal forming. From the calculated histories of stress and strain in each element, the fracture initiation site and the critical stroke are predicted by means of the ductile fracture criterion. The calculations are carried out for axisymmetric stretch forming of various aluminium alloy sheets and their laminates clad by mild steel sheets. The predictions so obtained are compared with experimental observations. The results show that the combination of the finite element simulation and the ductile fracture criterion enables the prediction of forming limit in a wide range of sheet metals. Accepted for publication 11 August 1996     

Load-Inversion Device for the High Strain Rate Tensile Testing of Sheet Materials with Hopkinson Pressure Bars

A high strain rate tensile testing technique for sheet materials is presented which makes use of a split Hopkinson pressure bar system in conjunction with a load inversion device. With compressive loads applied to its boundaries, the load inversion device introduces tension into a sheet specimen. Two output bars are used to minimize the effect of bending waves on the output force measurement. A Digital Image Correlation (DIC) algorithm is used to determine the strain history in the specimen gage section based on high speed video imaging. Detailed finite element analysis of the experimental set-up is performed to validate the design of the load inversion device. It is shown that under the assumption of perfect alignment and slip-free attachment of the specimen, the measured stress–strain curve is free from spurious oscillations at a strain rate of 1,000 s^?1. Validation experiments are carried out using tensile specimens extracted from 1.4 thick TRIP780 steel sheets. The experimental results for uniaxial tension at strain rates ranging from 200 s^?1 to 1,000 s^?1 confirm the oscillation-free numerical results in an approximate manner. Dynamic tension experiments are also performed on notched specimens to illustrate the validity of the proposed experimental technique for characterizing the effect of strain rate on the onset of ductile fracture in sheet materials.     

Evaluation of the VDA 238–100 Tight Radius Bend Test for Plane Strain Fracture Characterization of Automotive Sheet Metals

Accurate characterization of the fracture limit in plane strain tension of automotive sheet metals is critical for the design and crash performance of structural components. Plane strain bending using the VDA 238–100 V-bend test has potential for proportional fracture characterization by avoiding a tensile instability. The VDA 238–100 V-bend test was evaluated using DIC strain measurement to characterize the plane strain fracture limit under proportional plane stress loading and to evaluate the effect of the VDA pre-straining methodology for ductile alloys upon the material response. The load-based failure criterion of the V-bend test was evaluated with DIC to monitor the development of surface cracking. The influence of the non-linear strain path imposed by the pre-straining procedure for ductile materials was then evaluated for three automotive alloys: an advanced high strength dual phase steel, DP1180, a rare-earth magnesium, ZEK100, and an AA5182 aluminum. A fracture criterion based on the load threshold was reasonable for the three alloys considered. Pre-straining in uniaxial tension prior to plane strain bending affected each alloy differently. The DP1180 was not affected by the non-linear strain path whereas the cumulative equivalent strain for the AA5182 and ZEK100 increased by strains of 0.07 and 0.05 strain, respectively. The non-linear strain path within the VDA pre-straining methodology creates ambiguity in comparing the fracture limits of different materials. The plane strain fracture limit for proportional loading can be readily obtained in the V-bend test with DIC strain measurement.

     

Three-dimensional ductile fracture analysis with a hybrid multiresolution approach and microtomography

A modified-JIC test on CT (compact tension) specimens of an alloy (Ti-Modified 4330 steel) was carried out. The microstructure (primary and secondary inclusions) in the fracture process zone and fracture surface are reconstructed with a microtomography technique. The zig-zag fracture profile resulting from nucleation of microvoid sheets at the secondary population of inclusions is observed. Embedding the experimentally reconstructed microstructure into the fracture process zone, the ductile fracture process occurring at different length scales within the microstructure is modeled by a hybrid multiresolution approach. In combination with the large scale simulation, detailed studies and statistical analysis show that shearing of microvoids (the secondary population of voids) determines the mixed mode zig-zag fracture profile. The deformation in the macro and micro zones along with the interaction between them affects the fracture process. The observed zig-zag fracture profile in the experiment is also reasonably captured. Simulations can provide a more detailed understanding of the mechanics of the fracture process than experiments which is beneficial in microstructure design to improve performance of alloys.     

Design and identification of high performance steel alloys for structures subjected to underwater impulsive loading

Martensitic and austenitic steel alloys were designed to optimize the performance of structures subjected to impulsive loads. The deformation and fracture characteristics of the designed steel alloys were investigated experimentally and computationally. The experiments were based on an instrumented fluid–structure interaction apparatus, in which deflection profiles are recorded using a shadow Moiré technique combined with high speed imaging. Fractographic analysis and post-mortem thickness reduction measurements were also conducted in order to identify deformation and fracture modes. The computational study was based on a modified Gurson damage model able to accurately describe ductile failure under various loading paths. The model was calibrated for two high performance martensitic steels (HSLA-100 and BA-160) and an austenitic steel (TRIP-120). The martensitic steel (BA-160) was designed to maximize strength and fracture toughness while the austenitic steel (TRIP-120) was designed to maximize uniform ductility, in other words, to delay necking instability. The combined experimental–computational approach provided insight into the relationships between material properties (strength, uniform ductility, and post-necking ductility) and blast resistance of structures. In particular, the approach allowed identification of material/structure performances by identifying impulse-center deflection behavior and the impulse leading to panel fracture.     

Brittle fracture of precompressed steel as affected by hydrostatic pressure,temperature and strain concentration

Highly precompressed 1020 HR steel, 0.65 prestrain at 400°F (204°C), tested in nominally uniform tension at ?80°F (?62°C) fractures at about 110,000 psi (760 MN/m²) with less than 0.02 plastic strain. Yet the addition of a hydrostatic pressure of less than 7000 psi (48 MN/m²) converts this visually brittle fracture to a ductile one with appreciable necking. The explanation of this surprising experimental result is shown to follow directly and simply from the combination of a tensile stress criterion of fracture, strain concentration and the low tangent modulus of the stress-strain curve in tension beyond the Bauschinger transition region of a few percent of plastic strain. Temperature dependence and strain-rate dependence of brittle fracture similarly are predictable in an almost trivial manner from the appropriate stress-strain curves for different amounts of precompression. So also is the amazingly high ductility or fracture toughness of the most complex of perforated or notched statically loaded structures of mild steel in an undamaged or fully annealed state.     

Hf基非晶合金夹芯结构长杆弹的侵彻行为

为研究Hf基非晶合金的变形行为及高速侵彻性能,分别开展了Hf基非晶合金材料静动态力学性能和Hf基非晶合金夹芯结构长杆弹高速侵彻45钢靶体试验研究,并与45钢夹芯长杆弹侵彻结果进行对比。研究发现:Hf基非晶合金具有较高的断裂强度,断裂时伴随有能量释放现象;Hf基非晶合金夹芯长杆弹侵彻钢靶过程可分为3个阶段:开坑、夹芯结构侵彻和剩余弹体侵彻。Hf非晶合金在侵彻过程中发生了明显的释能反应,显著地增强了弹体毁伤效应,扩大了侵彻弹孔直径,增加了弹体侵彻深度和弹孔体积。在高速冲击下,Hf基非晶合金夹芯长杆弹表现出优异的侵彻性能,可以为非晶合金材料在高效毁伤领域的应用提供新思路。     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

布孔方式对孔洞材料宏观力学性能影响的研究

运用材料破坏过程分析MFPA2D系统,从细观力学和损伤力学角度,研究了布孔方式对孔洞材料宏观力学性能以及破坏机理的影响。在研究中,分别建立了三种含双孔、四孔以及多孔的正方形数值模型。双孔以沿试件垂直中心线重叠布置,沿试件水平中心线并列布置和沿试件对角线倾斜布置三种方式进行布孔,四孔以正方形和菱形两种布孔方式置于试件中央区域,多孔成排布置并使其相邻四孔成正方形和菱形镶嵌于试件中。然后对这三种试件分别进行了标准的单轴压缩数值试验。通过对试验结果的讨论,阐明了布孔方式对孔洞材料宏观力学行为和细观损伤机理的影响。结果表明:孔洞的相互作用既可以增强应力集中程度,也可以减弱应力集中程度;正方形布孔方式比菱形布孔方式使孔洞材料具有更高的承载能力;多孔材料的延性断裂行为是孔洞应力屏蔽作用和材料损伤局部化行为共同作用的结果。     

含圆孔缺陷三点弯曲梁动态焦散实验

应用新型数字激光动态焦散线实验系统,采用含预制裂纹的有机玻璃板试件进行落锤冲击实验,研究了含圆孔缺陷三点弯曲梁的动态断裂行为。通过实验得到了含圆孔缺陷三点弯曲梁裂纹尖端动态应力强度因子的变化情况、裂纹扩展速度的变化情况以及裂纹贯穿空孔的扩展情况等。实验结果表明:三点弯曲梁中的空孔位置对裂纹的扩展轨迹具有明显的导向作用;空孔位置的改变会影响三点弯曲梁的断裂时间;空孔位置的变化对空孔下方裂纹的扩展时间、扩展轨迹影响较小;在空孔位置居中的情况下,空孔上方裂纹的最大扩展速度大于空孔位置偏移时的情况。     

Numerical prediction of fracture in the Taylor test

A flat-nosed cylinder moving at a sufficiently high impact velocity in the classical Taylor test will always fracture. In this paper, fracture phenomena and fracture mechanisms in the Taylor test are investigated numerically based on a recently developed ductile fracture locus with the cut-off value for the negative stress triaxiality at −1/3. The impact velocity of the projectile ranges from 240 m/s to 600 m/s. The lower velocity is applied to a less ductile 2024-T351 aluminum alloy cylinder while the higher velocity is introduced for more ductile Weldox 460 E steel. Three distinct fracture modes are recreated numerically: the confined fracture inside the cylinder, the shear cracking on the lateral surface, and the petalling, all of which are consistent with experimental results presented in the open literature. It is found that a more ductile cylinder tends to fail by petalling while a less ductile one by shear cracking. Confined fracture is a common failure mode for both materials, which occurs in a wide range of the impact velocity. The ductile fracture criterion with the cut-off value predicts realistic fracture patterns for short cylinders deforming predominantly under compression.     

Predicting the failure of ultrasonic spot welds by pull-out from sheet metal

A methodology for determining the cohesive fracture parameters associated with pull-out of spot welds is presented. Since failure of a spot weld by pull-out occurs by mixed-mode fracture of the base metal, the cohesive parameters for ductile fracture of an aluminum alloy were determined and then used to predict the failure of two very different spot-welded geometries. The fracture parameters (characteristic strength and toughness) associated with the shear and normal modes of ductile fracture in thin aluminum alloy coupons were determined by comparing experimental observations to numerical simulations in which a cohesive-fracture zone was embedded within a continuum representation of the sheet metal. These parameters were then used to predict the load–displacement curves for ultrasonically spot-welded joints in T-peel and lap-shear configurations. The predictions were in excellent agreement with the experimental data. The results of the present work indicate that cohesive-zone models may be very useful for design purposes, since both the strength and the energy absorbed by plastic deformation during weld pull-out can be predicted quite accurately.     

Experimental and theoretical analysis of the limits to ductility of type 304 stainless steel sheet

The forming behaviour of type 304 stainless steel sheet has been investigated. The strain-hardening behaviour has been characterised in uniaxial tension tests, and the forming limits at necking and at fracture have been determined using the Marciniak punch test. The results, complemented by measurements of the fraction of martensite formed by plastic straining, have been compared with the predictions derived from the constitutive laws proposed by Iwamoto and Tsuta [Iwamoto, T., Tsuta, T., 2000. Computational simulation of the dependence of the austenitic grain size on the deformation behaviour of trip steels. Int. J. Plasticity 16, 791–804; Iwamoto, T., Tsuta T., 2002. Computational simulation on deformation behaviour of CT specimens of trip steel under mode I loading for evaluation of fracture toughness. Int. J. Plasticity 18, 1583–1606] for steels exhibiting transformation induced plasticity, and from a flow localisation analysis developed along the lines of the model of Marciniak and Kuczinski [Marciniak, Z., Kuczynski, K., 1967. Limit strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609–620]. A good account of the whole results can be obtained by considering the limits to ductility imposed by ductile fracture.     

Influence of calcium on cracking of steel during the welding or casting process

The influence of calcium on the brittle–ductile transition temperature is studied for the solidification range. The test bars were cast from carbon steel with and without the addition of calcium. Mechanical properties at different temperatures around the solidus were evaluated. The fractured surfaces were examined using a scanning microscope coupled with a Kevex analyser. For the modified steel, the liquid phase appears (on heating) for higher temperature while the temperature range within which fracture can nucleate, during casting or welding, is markedly narrowed. In medium-carbon steel, calcium changes the manner of fusion of the grains. The inclusions of the liquid phase form at the triple points and the surfaces of grains remain solid above the solidus temperature.     

金属材料中低加载速率下的动态韧脆转变及断裂韧性测量

金属材料在冲击下的韧脆转变现象和动态断裂韧性的测量是金属材料冲击力学性能研究的重要组成部分.针对金属材料在冲击下的韧脆转变现象认识不足和韧性材料在较低加载率下动态$J$-$R$阻力曲线难以测量的现状,提出了采用高速材料试验机, 设计专用试验夹具,测量15MnTi钢和11MnNiMo钢在不同加载速率下的韧脆转变过程,以及裂尖约束对其动态韧脆转变速率变化的影响.在高速材料试验机上采用上夹具辊刹车,通过调节压缩杆长度改变试验中裂纹扩展量的试验方法,测量了15MnTi钢三点弯曲试样件在较低加载率下的动态断裂韧性.试验发现15MnTi钢CT试验件加载速率低于0.025 m/s时呈现出韧性断裂的特点,加载速率在0.1,$\sim$,0.5 m/s时为韧脆结合型断裂,加载速率高于0.5 m/s后进入脆性断裂区; 11MnNiMo钢CT试验件加载速率大于1.5 m/s后,分层断裂过程中出现先脆断后韧段的现象;发现15MnTi钢和11MnNiMo的动态韧脆转变速率受裂尖约束的影响非常明显,面内约束和面外约束的升高都会导致材料动态脆断速率出现明显降低;还发现三点弯曲试验中, 15MnTi钢在8788 MPa$\cdot$mm/s加载率内断裂韧性随加载率的提升呈现出缓慢下降的趋势.      

Effects of stress invariants and reverse loading on ductile fracture initiation

Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.     

CRACK INTERACTING WITH AN INDIVIDUAL INCLUSION BY THE FRACTURE CRITERION OF CONFIGURATIONAL FORCE

基于构型力概念提出一种可判断裂纹起裂以及裂纹扩展方向的新断裂准则.该准则假设当构型合力值达到一个临界值时裂纹开始扩展,而裂纹扩展的方向则为构型合力的矢量方向.基于此断裂准则,本文开发构型力的有限元计算方法,实现对裂纹扩展的数值模拟,并着重对工程中常见的含孔洞/夹杂结构的裂纹扩展问题展开研究.研究结果表明,基于构型力的裂纹扩展准则可以很好地预测裂纹与孔/夹杂的干涉作用,其数值模拟结果与实验结果相符,从而验证了该裂纹扩展模拟方法的有效性.通过对裂纹和夹杂（圆孔、软夹杂、硬夹杂）干涉问题的数值模拟表明,裂纹前端夹杂对裂纹的扩展具有重要影响.裂纹的扩展方向与裂纹和夹杂的相对位置、以及夹杂类型密切相关.软夹杂和圆孔会吸引裂纹向其扩展,而硬夹杂会排斥裂纹扩展,裂纹在扩展过程中会绕开硬夹杂.当裂纹与夹杂夹角较小时,夹杂对裂纹扩展的影响作用明显,当夹角较大时,夹杂对裂纹扩展的影响较小;特别当裂纹与夹杂夹角为45°时,软夹杂和圆孔可能会抑制裂纹的扩展,使裂纹扩展发生止裂.研究结果有助于认清含孔洞/夹杂结构中的裂纹扩展或止裂问题,对于工程中的断裂问题具有重要指导意义.     

Characterizing void nucleation in a damage-based constitutive model using notched tensile sheet specimens

An experimental and numerical test programme was conducted to investigate damage-induced ductile fracture in notched tensile sheet specimens of an aluminum–magnesium alloy. An upper bound, damage-based constitutive model was employed to estimate the formability of the material over a range of stress states found in sheet metal forming. Stress- and strain-based nucleation models are evaluated to characterize damage initiation and fracture of the material. The ligament strain-to-failure, elongation-to-failure and load–displacement curves can be captured using either nucleation rule. The advantages of each nucleation model are discussed in relation to quantitative measurements of damage available in the literature. Stress-based nucleation provides a promising approach for characterizing the nucleation behaviour over a range of stress states compared to strain-based nucleation.     

影响三维编织CMC断裂性能的孔洞问题

在气相沉积三维编织陶瓷基复合材料(CMC)的编织结构中，孔洞的存在在所难免。研究孔洞对断裂性能的影响必须面对孔洞带来的问题。过去研究孔洞问题的工作主要集中在等效模量和强度上，并取得了一些理论成果。然而，除了微裂纹、纤维和偏转增韧等的研究外，很少有关于孔洞对断裂性能的文献报道。因此这里探讨一下孔洞对断裂的影响问题。通常研究者认为孔洞能够通过两种途径增韧材料的断裂韧性：即裂尖的钝化和材料柔性增加。前者只能够定性地认识和分析裂尖形貌的增韧效果(本文不涉及此内容)；后者可以做一些定量的分析。基于此，首先研究了孔洞的形态与分布，并给出了孔洞模型。其次用两次等效的工程方法均匀化材料的有效弹性模量，并且和实验相比较，其结果令人满意。接着又分析了应力强度因子K及K控制区随孔洞体积分量的变化规律。最后引用能量释放率G用图的形式表述了孔洞的增韧效果。显然图中的结论表明，孔洞的增韧效果并不理想。     

A linked FEM-damage percolation model of aluminum alloy sheet forming

A so-called damage percolation model is linked with a finite element model of a sheet forming process to offer a comprehensive study of ductile damage evolution. In the current study, a damage percolation code is linked with LS-DYNA, an explicit dynamic FEM code used to introduce local strain gradients and compliance effects due to damage-induced softening. The linked model utilizes a Gurson-based yield surface to account for the softening effects of void damage, while the local damage development and void linkage events are modeled using the damage percolation code. The percolation code accepts detailed second phase particle fields from image analysis of a 2.0×1.6 mm optical micrograph of AA5182 aluminum alloy sheet. The model is applied to a stretch-flange stamping process which is known to be a damage-sensitive operation. The critical conditions for fracture are predicted for various initial stretch flange hole sizes.