Visualization by X-ray tomography of void growth and coalescence leading to fracture in model materials

The literature contains many models for the process of void nucleation, growth and coalescence leading to ductile fracture. However, these models lack in-depth experimental validation, in part because void coalescence is difficult to capture experimentally. In this paper, an embedded array of holes is obtained by diffusion bonding a sheet filled with laser-drilled holes between two intact sheets. The experiments have been performed with both pure copper and Glidcop. Using X-ray computed tomography, we show that void growth and coalescence (or linkage) are well captured in both materials. The Brown and Embury model for void coalescence underestimates coalescence strains due to constraining effects. However, both the Rice and Tracey model for void growth and the Thomason model for void coalescence give good predictions for copper samples when stress triaxiality is considered. The Thomason model, however, fails to predict coalescence for the Glidcop samples; this is primarily due to secondary void nucleation.     

Ductile spallation fracture and the mechanics of void growth and coalescence under shock-loading conditions

A model of ductile spallation fracture is developed from a dynamic void-growth model which takes full account of the effects of material inertia and strain-rate sensitivity on void-growth rates under shock-loading conditions. The void-growth model is used to estimate the dynamic inertial stresses arising at incipient void coalescence and thus allow for these effects in the critical condition for dynamic microvoid coalescence. The theoretical results from the dynamic ductile-fracture model are shown to be in good general agreement with previously published experimental results for ductile spallation fracture in tantalum.     

Micromechanics-based model for trends in toughness of ductile metals

Relations between fracture toughness and microstructural details have been calculated for ductile materials based on a dilatational plasticity constitutive model that has recently been proposed. The model generalizes the Gurson model to account for both void growth and coalescence with explicit dependence on void shape and distribution effects. Based on a small scale yielding formulation of crack growth, toughness trends are determined as a function of yield stress, strain-hardening, initial porosity, void shape and spacing as well as void spacing anisotropy. Distinctions are drawn between the engineering fracture toughness, which is typically associated with 0.2 mm of crack growth, and the theoretical toughness based on coalescence of the crack tip with the first void ahead of it. Comparison with one set of experimental data for a steel is made for which a fairly complete characterization of the microstructure is available.     

A New Method to Calculate Threshold Values of Ductile Fracture Criteria for Advanced High-Strength Sheet Blanking

A new approach is presented in this paper to calculate the critical threshold value of fracture initiation. It is based on the experimental data for forming limit curves and fracture forming limit curves. The deformation path for finally a fractured material point is assumed as two-stage proportional loading: biaxial loading from the beginning to the onset of incipient necking, followed plane strain deformation within the incipient neck until the final fracture. The fracture threshold value is determined by analytical integration and validated by numerical simulation. Four phenomenological models for ductile fracture are selected in this study, i.e., Brozzo, McClintock, Rice-Tracey, and Oyane models. The threshold value for each model is obtained through best-fitting of experimental data. The results are compared with each other and test data. These fracture criteria are implemented in ABAQUS/EXPLICIT through user subroutine VUMAT to simulate the blanking process of advanced high-strength steels. The simulated fracture surfaces are examined to determine the initiation of ductile fracture during the process, and compared with experimental results for DP780 sheet steel blanking. The comparisons between FE simulated results coupled with different fracture models and experimental one show good agreements on punching edge quality. The study demonstrates that the proposed approach to calculate threshold values of fracture models is efficient and reliable. The results also suggest that the McClintock and Oyane fracture models are more accurate than the Rice-Tracey or Brozzo models in predicting load-stroke curves. However, the predicted blanking edge quality does not have appreciable differences.     

Internal ductile failure mechanisms in steel cold heading process

The occurrence of internal ductile failure in cold-headed products presents a major obstacle in the fast expanding cold heading (CH) industry. This internal failure may lead to catastrophic brittle fracture under tensile loads despite the ductile nature of the material. Comprehensive testing and investigation methodologies were used to this work to reveal the complicated interplay of process and material parameters contributing in the initiation and propagation of internal ductile failure in six CH quality AISI steel grades.The metallurgical and microscopic investigations showed that internal ductile failure occurs progressively by void nucleation and growth mechanisms with increasing plastic strain inside the highly localized adiabatic shear bands (ASBs). The void nucleation occurs by decohesion at second-phase particles, inclusion–matrix interfaces, grain boundaries and by particle or inclusion cracking. Therefore, the number and morphology of any inclusions and second-phase particles are key factors in material formability.The metallurgical investigations showed that under compressive loading conditions, the nature of the metal flow pattern promotes different rates of material flow around the inclusions and stringers which supports decohesion and void nucleation since the early stages of deformation. At advanced stages of deformation, the metal flow pattern contributes to the ASB localization in supporting void growth and coalescence along the band leading to narrow void sheets.All tested materials in this work experienced ductile failure by void nucleation and coalescence, forming cracks along the ASBs. The ductile failure of each material was the result of the contribution of all the mechanisms of void nucleation at the inclusion–matrix interface, second phase–matrix interface and at the grain boundaries. However, the level of contribution of each mechanism in the final ductile failure varied depending on material properties and their microstructure.     

The characterization and interpretation of ductile fracture mechanisms in AL2024-T351 using X-ray and focused ion beam tomography

This paper describes an experimental investigation into the mechanism of ductile fracture in the aluminum alloy AL2024-T351 using a combination of synchrotron X-ray and focused ion beam tomography. Microstructural features that influence fracture at the micro- and nanoscale were characterized in virgin material in three-dimensions. The nature and volume fraction of ductile damage was then quantified as a function of distance below the fracture surfaces of tested notched and fatigue pre-cracked laboratory specimens. In both specimens the ductile fracture process initiates with the brittle fracture of large irregular intermetallic particles at low levels of plastic strain. With increasing plasticity, the resulting voids grow and combine with pre-existing porosity to increase the overall void volume fraction. Once a critical void volume fraction is attained, final failure occurs by the fracture or decohesion of dispersoids from the matrix, initiating a second population of nanoscale voids, which interlinks the larger voids. The critical void volume fraction for coalescence and the distribution of ductile damage below the fracture surface is markedly different between blunt-notched and pre-cracked specimens, with notched specimens exhibiting a significantly lower critical void volume fraction and a more extensive distribution of ductile damage below the fracture surface than is observed in pre-cracked specimens. This observation, related to the gradients in stress triaxiality and plastic strain in each specimen type, has important implications for the calibration of ductile damage mechanics models against notched-specimen data and their use to predict crack behavior in engineering structures.     

Effect of triaxiality on void growth and coalescence in model materials investigated by X-ray tomography

Void growth and coalescence/linkage, which play significant roles during ductile fracture processes, are strongly influenced by stress triaxiality in a deforming solid. The stress state can be changed by cutting notches in a tensile sample. In the current paper, void growth and linkage of an artificial void array embedded in a notched model material was studied by X-ray computed tomography, coupled with in situ tensile deformation. The cross-sectional shape of the tensile specimens was square, and a pair of notches was cut along only one direction. Thus, the lateral principal stress does not have an isotropic distribution: the principal stress along the notch direction is considered to be higher. This technique allowed us to explore the entire process of growth and linkage events of a void array embedded in a metal matrix. The notch effect creates a marked acceleration in void growth, leading to a large reduction in the linkage strains, as compared with similarly fabricated unnotched samples. The standard models for coalescence could not provide consistent predictions of the measured notch effect.     

Performance evaluation of HSLA steel subjected to underwater explosion

Performance evaluation of High Strength Low Alloy (HSLA) steel subjected to underwater explosion is of interest to materials engineers because of its structural applications in ships and submarines. Circular and rectangular plates were investigated for their explosive response because they represent panels of a ships plating. Underwater explosion bulge tests were carried out with increasing shock intensity on 4 mm thick circular plates of 290 mm diameter and rectangular plates of 300×250 mm to study the plastic deformation and the onset of fracture. Empirical models were developed for the prediction of depth of bulge of the plates. A fresh set of tests with various explosive charge quantities and stand offs were carried out which showed good agreement with the models. Failed edges of the plate showed slant fracture suggesting ductile mode of failure. Scanning Electron Microscopic (SEM) fractographic examination showed dimple features suggesting micro void coalescence.     

Onset of void coalescence in uniaxial tension studied by continuous X-ray tomography

Void growth and coalescence in model materials containing a pre-existing three-dimensional void array were studied by X-ray computed tomography coupled with in situ uniaxial tensile deformation. A newly developed continuous tomography technique was employed to capture the onset of coalescence. Using a picosecond laser machining system and a diffusion bonding technique, model materials with different void geometries were prepared. By implementing continuous tomography, the plastic strain at the onset of void coalescence was measured (instead of simple linkage) for the first time. The plastic strains at the onset of void coalescence were compared with the existing void coalescence models. Finite-element (FE) simulations were performed to study the influences of void shape (sphere, cylinder, tapered-cylinder) on the void growth behavior. This study shows that the coalescence models developed by Thomason and later extended by Pardoen and Hutchinson provide accurate predictions of coalescence strain when the voids are aligned normal to the tensile axis. However, offsets can induce shear effects that lower the coalescence strain in a manner not predicted by the models. Two-dimensional plane-strain FE simulations were also used to explore the influence of shear localization between two misaligned coalescing voids on ductility. These demonstrate the nature of the effect.     

AISI-1035钢精冲成形与断裂的数值模拟

使用DEFORM2D软件对AISI-1035钢的落料、冲孔精冲工艺进行了弹塑性大变形有限元数值模拟,将McClintock断裂准则应用于精冲韧性断裂的预测中,预测了材料变形过程中静水应力、等效应力和等效应变的分布以及发展趋势、精冲最后阶段微裂纹产生发展和最终断裂。     

空穴长大延性损伤新模型

以45中碳钢为研究对象,进行了拉伸、压缩、扭转、精冲实验,并结合有限元对各实验过程中的应力三轴度和延性损伤进行了分析,归纳了金属材料的3种延性损伤机理:无空穴影响剪切损伤、剪切型空穴损伤和拉伸型空穴损伤.在上述工作基础上,提出了一个新的基于空穴长大的延性损伤模型,能够较准确地预测材料拉伸、精冲过程中延性断裂的出现,扩大了损伤模型的预测范围.     

汽车用先进高强钢韧性断裂模型的研究与应用进展

韧性断裂预测对汽车轻量化产品设计与成形工艺优化有着重要的意义.全面综述了强耦合型与弱(非)耦合型韧性断裂模型的发展与研究现状;重点围绕考虑加载路径与应力状态的断裂失效与成形极限曲线预测、各向异性耦合的失效模型拓展、应变速率与温度效应对材料断裂的影响等3个方面的研究现状及应用效果进行了分析介绍,其中,MMC模型、Lou-...     

Modeling vapor pressure effects on void rupture and crack growth resistance

The phenomenon of vapor pressure assisted void growth and rupture is studied. Plastic electronic packages absorb moisture which condenses within numerous micropores in the substrate, solder mask and die attach materials as well as near their interfaces. During reflow soldering, the condensed moisture vaporizes with the result that these micropores as well as interfaces are subjected to high vapor pressure. Under extreme conditions, our study suggests that vapor pressures can attain high enough levels to drive the voids to grow to rupture, thereby causing package failure. Under other conditions, residual/thermal stresses assisted by vapor pressure can cause crack growth within the polymeric materials as well as along interfaces. Vapor pressure effects on void growth have been incorporated into the Gurson model for porous ductile material. Using this model, a finite element study shows that the combination of high vapor pressure and high porosity is very detrimental to fracture toughness.     

Three-dimensional quantitative in situ study of crack initiation and propagation in AA6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations

Ductile crack initiation and propagation in AA6061 aluminum alloy for a fatigue precrack have been studied in situ via synchrotron radiation computed laminography, a technique specifically developed for three-dimensional imaging of laterally extended sheet specimens with micrometer resolution. The influence of the microstructure, i.e. due to the presence of coarse Mg₂Si precipitates and iron-rich intermetallics, on the void nucleation process is investigated. Coarse Mg₂Si precipitates are found to play a preponderant role in the void nucleation and ductile fracture process. Void growth and void coalescence are then observed and quantified by three-dimensional image analysis during crack initiation and propagation. Parameters for a Gurson–Tvergaard–Needleman micromechanical damage model are identified experimentally and validated by finite-element simulations.     

基于金属粉末压制模型的韧性损伤模型

以Lee多孔材料屈服模型为基础 ,并假设空穴密度积累到一临界值时 ,材料出现裂纹 ,推导出适用于多孔材料的韧性损伤模型。该模型描述了在应力、应变、密度分布及其积累因素影响下 ,材料的损伤状态。使用该模型可以跟踪整个加载过程中多孔材料各点的损伤状况和破裂过程。     

非线性路径下板料拉深成形过程中破裂预测

在优选模型参数和简化孔洞形核规律的基础上,采用Gurson—Tvergaard（GT）多孔材料本构模型分析圆筒件拉深过程;根据金属成形工艺特点,综合考虑拉伸型和剪切型2种不同韧性断裂机制,提出一个统一的韧性断裂准则形式。对于未经过预变形和经过预变形的圆筒件拉深试验和数值模拟进行了比较,结果表明：相对于成形极限图,新的韧性断裂准则可以更加准确地预测非线性路径下圆筒件的拉深破裂。     

Modeling of ductile-mode material removal in rotary ultrasonic machining

In rotary ultrasonic machining of ceramic materials there exist two modes of material removal: brittle fracture mode and ductile mode. Two models were developed based on the assumption that the brittle fracture is the dominating mode of material removal, and were published previously. This paper presents the follow-up work on modeling of the ductile-mode material removal in rotary ultrasonic machining. After a brief review of the ductile phenomena in ceramic machining, an approach to modeling the ductile-mode removal in rotary ultrasonic machining is proposed. Then, magnesia stabilized zirconia is used to demonstrate the model's capability of predicting the material removal rate from the process parameters and the material property of the workpiece. Finally, the results of the pilot experiments to verify the model are discussed.     

Pore size scaling for enhanced fracture resistance of nanoporous polymer thin films

Poly(arylene) ether (PAE) polymer films containing controlled nanometer-sized pores are shown to exhibit increasing fracture resistance with porosity. Such surprising behavior is in stark contrast to widely reported behavior for the fracture toughness of porous solids, which decreases markedly with porosity. A ductile nano-void growth and coalescence fracture mechanics-based model is presented to rationalize the increase in fracture resistance of the voided polymer film. The model is shown to explain the behavior in terms of a specific scaling of the size of the pores with pore volume fraction. It is demonstrated that the pore size must increase with close to a linear dependence on the volume fraction in order to increase rather than decrease the fracture energy. Independent characterization of the pore size as a function of volume fraction is shown to confirm predictions made by the model. Implications for the optimum void size and volume fraction are considered for superior fracture resistance of the nanoporous films.     

Experimental investigation of void coalescence in a dual phase steel using X-ray tomography

In situ tensile tests were carried out during X-ray microtomography imaging of a smooth and a notched specimen of dual phase steel. The void coalescence was first qualitatively observed and quantitative data concerning this damage step was then acquired. The void coalescence criteria of Brown and Embury and of Thomason were then tested against the experimental data at both the macroscopic and local levels. Although macroscopic implementation of the criteria gave acceptable results, the local approach was probably closest to the real nature of void coalescence, because it takes into account local coalescence events observed experimentally before final fracture. The correlation between actual coalescing couples of cavities and local implementation of the two criteria showed that the Thomason criterion is probably the best adapted to predict the local coalescence events in the case of the material studied.