A Shear Compression Disk Specimen with Controlled Stress Triaxiality Under Dynamic Loading

This paper presents an experimental and numerical study of the potential of the Shear Compression Disk specimen (SCD) to characterize the plastic flow and fracture of metals under various levels of stress triaxiality at strain rates of up to 10⁴ 1/s. The main loading mode in that specimen is shear with triaxiality ranging from 0 to -0.8. The specimen is relatively small and fits into a standard split Hopkinson pressure bar system. Aluminum 7075-T651 alloy was chosen for a test case study. Experimental and numerical investigations reveal the adequacy of the SCD specimen for the study of mechanical properties of materials under high strain-rates and low, though wide, range of stress triaxialities.     

Experimental and Numerical Analysis of an In-Plane Shear Specimen Designed for Ductile Fracture Studies

An in-plane shear specimen made of dual phase steel designed for ductile fracture studies is presented and then analyzed experimentally and numerically. In the experiment, digital image correlation (DIC) technique is utilized to measure the deformation of the specimen. Based on the implicit nonlinear FE solver Abaqus/Standard, numerical analysis of the specimen is performed by using plane stress and solid elements respectively. The elongation of the specimen’s gauge length and the shear strain distribution within the shear zone are compared between the experimental and numerical results and a general good agreement is obtained. Thereafter, based on calculated results, the stress state of the shear zone is investigated in detail. It is shown that the shear stress is dominant within the shear zone despite of the emergence of normal stresses. The deformation is concentrated in the shear zone, where the incipient fracture is most likely to occur. The stress triaxiality and the Lode parameter at the fracture initiation are found to be maintained at a relatively low level, which implies that the stress state achieved by the specimen is close to pure shear. The present study demonstrates that the proposed in-plane shear specimen is suitable for investigation of the fracture behavior of high strength materials under shear stress states.     

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.      

EVALUATION OF DUCTILE FRACTURE CRITERIA IN A GENERAL THREE-DIMENSIONAL STRESS STATE CONSIDERING THE STRESS TRIAXIALITY AND THE LODE PARAMETER

This paper is concerned with evaluation of various ductile fracture criteria in a general three-dimensional stress state of stress triaxiality, the Lode parameter and the equiva- lent plastic strain to fracture. Evaluation is carried out by comparing fracture loci constructed by fracture criteria to experimental results of A12024-T351. Comparison demonstrates that the Modified Mohr-Coulomb criterion and a newly proposed criterion provide sufficient predictabil- ity of fracture strain. Moreover, evaluation is emphasized on the predicted cut-off value for stress triaxiality. The evaluation demonstrates that the Cockcroft-Latham, Brozzo, Oh, Ko-Huh and the new criteria coupled a reasonable cut-off value for ductile materials.     

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.     

A Ductile Fracture Criterion of Ti-6Al-4V at Room Temperature

The workability diagram is often used for predicting ductile fracture in metal forming processes. The shape of this diagram is usually determined experimentally by means of several tests. These tests should provide the strain to fracture at different values of the stress triaxiality. For ductile materials, it is difficult to get the shape of the diagram at small (algebraically) values of the stress triaxiality and it is not necessary for many applications. However, for low ductility metals, such as titanium alloys, it is important to propose and carry out tests in which the stress triaxiality is much smaller than in typical tests used to determine the workability diagram. Such a test is proposed and carried out in the present paper. Then, several standard upsetting tests are performed to determine the workability diagram of Ti-6Al-4V in a wide range of the stress triaxiality. The workability diagram is converted into the strain based formability diagram using a theoretical method available in the literature.     

Shear Testing of Polypropylene Materials Analysed by Digital Image Correlation and Numerical Simulations

Distributions of shear strains and strain states (triaxiality) were analysed for two in-plane shear test fixtures (Iosipescu and V-notched rail), using digital image correlation and numerical simulations. Three different polypropylene-based materials (two talc-filled compounds and one unfilled homopolymer) were tested. The three materials behaved differently in the shear tests. Most notably, cracks developed in tension near the notches for the particle-filled materials, while the unfilled homopolymer did not fracture. There were also differences between the materials regarding strain localisation between the notches, strain rates vs. strain level (for a given cross-head speed), thickness change in the sheared section, and triaxiality. The yield stresses in shear, uniaxial tension and uniaxial compression showed pressure sensitivity. At least for equivalent strain rates below 1?s^?1, the strain rate sensitivity of the yield stress was approximately the same in these three stress states. The stress?Cstrain curves obtained with the two methods were quite similar for these materials. There were some differences between the methods regarding the ease of mounting and aligning specimens, the complexity of specimen deformation patterns, and the uniformity of the shear strain distribution between the notches.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.     

金属材料脆性断裂机理的实验研究

材料的脆性断裂有许多准则和模型,但对脆断机理和变化规律缺乏合理的描述,给工程应用带来不便。本文对典型脆性材料球墨铸铁、灰铸铁分别进行了拉扭双轴断裂实验和常规拉伸、扭转破坏实验;对韧性金属材料合金钢进行了单轴拉伸颈缩破坏实验。通过上述实验分析了脆性材料和韧性材料发生脆性断裂的机理特征并选择应力三维度作为应力状态参数描述危险点的应力状态,同时考察了脆性材料和韧性材料发生脆性断裂的主导因素。结果表明:韧性材料45#钢和14CrNiMoV合金钢在颈缩断面心部应力三维度值较大时发生脆性拉断,而在颈缩断面边缘处应力三维度值较小时发生剪断;脆性材料球墨铸铁在应力三维度值为0.0～0.33之间变化时均发生脆性断裂;灰铸铁在应力三维度值大于0.0时发生脆性拉断,而在应力三维度值小于0.0时发生剪断。因此可以认为,材料的细观组织结构和危险点应力状态是影响断裂机理及变化规律的主要因素。对于同种材料,随着应力三维度代数值从小向大变化材料的断裂机制由塑性剪切断裂逐渐转变为脆性断裂。本文通过对几种材料的脆性断裂危险点和断裂方向的研究给出了脆断宏观破坏条件。     

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。     

Modification of the Gurson Model for shear failure

Recent experimental evidence points to limitations in characterizing the critical strain in ductile fracture solely on the basis of stress triaxiality. A second measure of stress state, such as the Lode parameter, is required to discriminate between axisymmetric and shear-dominated stress states. This is brought into the sharpest relief by the fact that many structural metals have a fracture strain in shear, at zero stress triaxiality, that can be well below fracture strains under axisymmetric stressing at significantly higher triaxiality. Moreover, recent theoretical studies of void growth reveal that triaxiality alone is insufficient to characterize important growth and coalescence features. As currently formulated, the Gurson Model of metal plasticity predicts no damage change with strain under zero mean stress, except when voids are nucleated. Consequently, the model excludes shear softening due to void distortion and inter-void linking. As it stands, the model effectively excludes the possibility of shear localization and fracture under conditions of low triaxiality if void nucleation is not invoked. In this paper, an extension of the Gurson model is proposed that incorporates damage growth under low triaxiality straining for shear-dominated states. The extension retains the isotropy of the original Gurson Model by making use of the third invariant of stress to distinguish shear dominated states. The importance of the extension is illustrated by a study of shear localization over the complete range of applied stress states, clarifying recently reported experimental trends. The extension opens the possibility for computational fracture approaches based on the Gurson Model to be extended to shear-dominated failures such as projectile penetration and shear-off phenomena under impulsive loadings.     

Comparison of ductile fracture properties of aluminum castings: Sand mold vs. metal mold

This paper compares mechanical properties of two types of cast aluminum components made in sand molds and cast iron molds, respectively. For each type of the castings, a total of 12 fracture tests are performed under a wide range of stress states including 6 tensile tests on notched and unnotched round bars and 6 biaxial loading tests on butterfly specimens. Using a combined experimental–numerical approach, the plasticity and fracture properties of the components are characterized in terms of the true stress–strain curve and the ductile fracture locus. It is found that the sand-molding component is of higher yield resistance and lower ductility than the metal-molding one. Meanwhile, the fractographic study reveals that there exist two competing failure mechanisms: the internal necking of the matrix at high positive stress triaxialities and void sheeting due to shear at negative stress triaxialities. The transition of the failure modes occurs in the intermediate range. This suggests that a ductile fracture locus formulated in the space of the stress triaxiality and the effective fracture strain consist of three branches rather than a monotonic curve.     

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.     

Empirical assessment of ductile fracture initiation in steel bars with notch and three-point bend specimen with edge crack

Proposed is a parameter defined to characterize the onset of macrocrack initiation in notched steel bars and cracked three-point bend specimens. It accounts for stress triaxiality and damage by plasticity reflected via the effective plastic strain. Results are obtained for notched round bars made of 20#, A3, DE36I and DE36II steel by assuming that the stress triaxiality increases with increasing effective plastic strain; they are compared with the results by letting the stress triaxiality to be constant. Use are made of experimental data on the necking of tensile bars. The parameter corresponding to the onset of ductile fracture were found to be nearly constant. Since the local effective plastic stress can be related to the crack tip opening (COD) distance, the same procedure can be applied to evaluate fracture initiation in three-point bend specimens with an edge crack. It is found that the COD in AS1204-350 and AS1405-180 structural steels decreased with increasing stress triaxiality.     

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.

     

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。     

Determination of Early Flow Stress for Ductile Specimens at High Strain Rates by Using a SHPB

In a dynamic experiment to obtain the high-rate stress–strain response of a ductile specimen, it takes a finite amount of time for the strain rate in the specimen to increase from zero to a desired level. The strain in the specimen accumulates during this strain-rate ramping time. If the desired strain rate is high, the specimen may yield before the desired rate is attained. In this case, the strain rates at yielding and early plastic flow are lower than the desired value, leading to inaccurate determination of the yield strength. Through experimentation and analysis, we examined the validity and accuracy of the flow stresses for ductile materials in a split Hopkinson pressure (SHPB) bar experiment. The upper strain-rate limit for determining the dynamic yield strength of ductile materials with a SHPB is identified.     

半结晶聚合物损伤演化的实验表征与数值模拟

损伤本构模型对研究材料的断裂失效行为有重要意义, 但聚合物材料损伤演化的定量表征实验研究相对匮乏. 通过4种高密度聚乙烯(high density polythylene, HDPE)缺口圆棒试样的单轴拉伸实验获得了各类试样的载荷-位移曲线和真应力-应变曲线, 采用实验和有限元模拟相结合的方法确定了HDPE材料不同应力状态下的本构关系, 并建立了缺口半径与应力三轴度之间的关系;采用两阶段实验法定量描述了4种HDPE试样单轴拉伸过程中的弹性模量变化, 并建立了基于弹性模量衰减的损伤演化方程, 结合中断实验和扫描电子显微镜分析了应力状态对HDPE材料微观结构演化的影响. 结果表明缺口半径越小, 应力三轴度越大, 损伤起始越早、演化越快; 微观表现为: 高应力三轴度促进孔洞的萌生和发展, 但抑制纤维状结构的产生;基于实验和有限元模拟获得的断裂应变、应力三轴度、损伤演化方程等信息提出了一种适用于聚合物的损伤模型参数确定方法, 最后将本文获得的本构关系和损伤模型用于HDPE平板的冲压成形模拟, 模拟结果与实验结果吻合良好.      

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。     

Tension–torsion fracture experiments—Part I: Experiments and a procedure to evaluate the equivalent plastic strain

Ductile failure experiments on a double notched tube (DNT) specimen subjected to a combination of tensile load and torque that was applied at a fixed ratio is presented. The experimental results extend those in Barsoum and Faleskog (2007a) down to zero stress triaxiality. A new and robust evaluation procedure for such tests is proposed, and a simple relation for the equivalent plastic strain at failure for combined normal and shear deformation, respectively, is developed. Tests were carried out on the medium strength medium hardening steel Weldox 420, and the high strength low hardening steel Weldox 960. The experimental results unanimously show that ductile failure not only depends on stress triaxiality, but is also strongly affected by the type of deviatoric stress state that prevails, which can be quantified by a stress invariant that discriminates between axisymmetric stressing and shear dominated stressing, e.g., the Lode parameter. Additional experiments on round notch bar (RNB) specimens are recapitulated in order to give a comprehensive account on how ductile failure depends on stress triaxiality, ranging from zero to more than 1.6, and the type of stress state for the two materials tested. This provides an extensive experimental data base that will be used to explore an extension of the Gurson model that incorporates damage development in shear presented in Xue et al. (2013) (Part II).