DETERMINATION OF FRACTURE TOUGHNESS OF BRITTLE MATERIALS BY INDENTATION

Fracture toughness is one of the crucial mechanical properties of brittle materials such as glasses and ceramics which demonstrate catastrophic failure modes. Conventional standardized testing methods adopted for fracture toughness determination require large specimens to satisfy the plane strain condition. As for small specimens, indentation is a popular, sometimes exclusive testing mode to determine fracture toughness for it can be performed on a small flat area of the specimen surface. This review focuses on the development of indentation fracture theories and the representative testing methods. Cracking pattern dependent on indenter geometry and material property plays an important role in modeling, and is the main reason for the diversity of indentation fracture theories and testing methods. Along with the simplicity of specimen requirement is the complexity of modeling and analysis which accounts for the semi-empirical features of indentation fracture tests. Some unresolved issues shaping the gap between indentation fracture tests and standardization are also discussed.     

Erratum to: Rock Dynamic Fracture Toughness Tested with Holed-Cracked Flattened Brazilian Discs Diametrically Impacted by SHPB and its Size Effect

Dynamic fracture initiation toughness of marble was tested using two types of the holed-cracked flattened Brazilian disc (HCFBD) specimens, which were diametrically impacted at the flat end of the disc by the split Hopkinson pressure bar (SHPB) of 100 mm diameter. One type of the discs is geometrically similar with different outside diameter of 42 mm, 80 mm, 122 mm and 155 mm respectively, and with crack length being half the diameter; another type of the discs has identical 80 mm diameter and different crack length. Issues associated with determination of the stress wave loading by the SHPB system and the crack initiation time in the disc specimen were resolved using strain gage technique. The stress waves recorded on the bars and the disc failure patterns are shown and explained. The tested dynamic fracture toughness increases obviously with increasing diameter for the geometrically similar HCFBD specimens. It changes moderately for the one-size specimens of identical diameter and different crack length. The size effect of rock dynamic fracture toughness is mainly caused by the fracture process zone length l and fracture incubation time τ, the latter being an additional influencing factor for the dynamic loading as compared with the counterpart static situation. Hence a method is proposed to determine a unique value for the dynamic fracture initiation toughness, the approach takes average of the local distribution and time history for dynamic stress intensity factor in the spatial-temporal domain, which is defined by l and τ jointly. In this way the dynamic size effect is minimized.     

皮质骨断裂力学行为的实验研究

采用稳态裂纹扩展和疲劳裂纹扩展的实验, 研究了牛皮质骨横向和纵向裂纹扩展的断裂力学行为. 沿着两个方向制备了紧凑拉伸(CT)试件. 由于试件尺寸的限制,采用数值计算方法确定了裂纹尖端应力强度因子与裂纹长度的关系. 在实验中, 采用数字图像相关法精确测定裂纹尖端的位置. 由于裂纹沿横向扩展时有较大的偏斜, 将采用$J$积分测量其断裂韧性. 实验结果表明, 在裂纹扩展的一定范围内, 皮质骨的断裂韧度随着裂纹不断扩展而增大, 即表现出上升的阻力曲线(R-curve)性质.而皮质骨的横向裂纹扩展的断裂韧度要远远大于纵向裂纹扩展的断裂韧度, 表现出各向异性的阻力曲线行为. 在疲劳裂纹扩展中, 纵向疲劳裂纹扩展率要大于横向疲劳裂纹扩展率, 这说明皮质骨具有各向异性的疲劳裂纹扩展性质.      

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

Tensile and Tensile-Mode Fatigue Testing of Microscale Specimens in Constant Humidity Environment

A tensile and tensile-mode-fatigue tester has been developed for testing microscale specimens in high humidity environments in order to investigate the fracture mechanisms of microelectromechanical materials. A humidity control system was installed on a tensile-mode fatigue tester equipped with an electrostatic force grip. A specimen and a griping device were inserted into a small chamber and the humidity was controlled by air flow from a temperature and humidity chamber. The humidity stability was within ±2%RH for humidities in the range 25–90%RH for eight hours of testing. Fatigue tests were performed on single-crystal silicon (SCS) specimens in constant humidity environments and laboratory air for up to 10⁶ cycles. The gauge length, width, and thickness of the SCS specimens were 100 or 500 μm, 13.0 μm, and 3.3 μm, respectively. The average tensile strength was 3.68 GPa in laboratory air; this value decreased in high humidity environments. Fatigue failure was observed during cyclic loading at stresses lower than the average strength. A reduction in the fatigue strength was observed at high relative humidities. Different fracture origins and fracture behaviors were observed in tensile tests and fatigue tests, which indicates that the water vapor in air affects the fatigue properties of SCS specimens.     

40Cr材料动态起裂韧性KId（）的实验测试

描述了利用Ｈｏｐｋｉｎｓｏｎ压杆技术加载三点弯曲试样测试４０Ｃｒ，材料动态起裂韧性ＫＩｄ（）的试验方法。试样上的动态载荷历程由Ｈｏｐｋｉｎｓｏｎ杆直接测得，并分别代入动态有限元程序及近似公式求得动态应力强度因子历史；由贴在试样裂尖附近的应变片确定起裂时间，最终确定起裂时的动态应力强度因子值，即动态起裂韧性ＫＩｄ（）。试验结果表明:利用Ｈｏｐｋｉｎｓｏｎ压杆技术加载三点弯曲试样测试材料动态起裂韧性的方法是可行的，起裂时，动态有限元的位移法、应力法及近似公式法求得的动态应力强度因子值比较吻合；在本文的载荷速率下，４０Ｃｒ材料动态起裂韧性ＫＩｄ（）与准静态裂韧性ＫＩｄ（）相比，降低了约２８％。     

Fracture toughness for CNT specimens from numerically obtained critical CTOD values

Many approaches for estimating mode I fracture toughness (K_IC) using circumferentially notched tensile (CNT) specimen have been demonstrated in the literature. In this paper, an effective approach for estimating fracture toughness from the numerical solution of critical crack tip opening displacement (CTOD) is proposed. An elasto-plastic finite element analysis is used to estimate critical CTOD values for CNT specimens. A number of materials are analysed, and the relationship between K_IC and critical CTOD for CNT specimens is obtained. The proposed relationship is validated by comparing the fracture toughness values obtained from the relationship with those obtained experimentally using CNT specimens. The fracture toughness (K_IC) calculated according to this relationship from numerically obtained critical CTOD is found to be in close agreement with the experimentally obtained fracture toughness for the respective materials.     

评估材料断裂韧性的损伤等效法

以实际结构充实验试件与ＨＲＲ裂尖场的一特征点的损伤相当为原则，建立了ＨＲＲ场的裂尖控制参数与实际试件在结构裂尖控制参数之间的关系．据此可消除不同试件因约束不同而导致的断裂韧性的变化；亦可用来评估实际结构及试件的断裂失效。     

Effect of intrinsic stress gradient on the effective mode-I fracture toughness of amorphous diamond-like carbon films for MEMS

The influence of intrinsic stress gradient on the mode-I fracture of thin films with various thicknesses fabricated for Microelectromechanical Systems (MEMS) was investigated. The material system employed in this study was hydrogen-free tetrahedral amorphous diamond-like carbon (ta-C). Uniform gauge microscale specimens with thicknesses 0.5, 1, 2.2, and 3 μm, containing mathematically sharp edge pre-cracks were tested under mode-I loading in fixed grip configuration. The effective opening mode fracture toughness, as calculated from boundary force measurements, was 4.25±0.7 MPa√m for 0.5-μm thick specimens, 4.4±0.4 MPa√m for 1-μm specimens, 3.74±0.3 MPa√m for 2.2-μm specimens, and 3.06±0.17 MPa√m for 3-μm specimens. Thus, the apparent fracture toughness decreased with increasing film thickness. Local elastic property measurements showed no substantial change as a function of film thickness, which provided evidence for the stability of the sp²/sp³ carbon binding stoichiometry in films of different thicknesses. Detailed experiments and finite element analysis pointed out that the dependence of the effective fracture toughness on specimen thickness was due to the intrinsic stress gradient developed during fabrication and post-process annealing. This stress gradient is usually unaccounted for in mode-I fracture experiments with thin films. Thicker films, fabricated from multiple thin layers, underwent annealing for extended times, which resulted in a stress gradient across their thickness. This stress gradient caused an out-of-plane curvature upon film release from its substrate and, thus, combined bending and tensile mode-I loading at the crack tip under in-plane forces. Since the bending component cannot be isolated from the applied boundary force measurements, its contribution, becoming important for thick films, remains unaccounted for in the calculation of the critical stress intensity factor, thus resulting in reduced apparent fracture toughness that varies with film thickness and curvature. It was concluded that in the presence of a stress gradient, accounting only for the average intrinsic stresses could lead in an overestimate of the fracture resistance of a brittle film. Under these considerations the material fracture toughness of ta-C, as determined from specimens with negligible curvature, is K_IC=4.4±0.4 MPa√m.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

岩石动态断裂韧度的尺寸效应

采用两种圆孔裂缝平台巴西圆盘试件(一种为直径分别为42、80、122、155 mm的几何相似试件,另一种为直径80 mm、仅裂缝长度不同的单一尺寸试件)对岩石动态断裂韧度的尺寸效应进行了研究。给出了在霍普金森压杆系统上对试件进行径向撞击产生的应变波形和断裂模式。实验结果表明,对于几何相似试件,动态断裂韧度的测试值随着尺寸的增大而增大,而对于单一尺寸试件,其测试值随着中心裂缝长度的增加呈现先增大后减小的趋势。裂缝前端的断裂过程区长度和孕育时间是岩石动态断裂韧度测试值表现为尺寸效应的主要原因,为了减小尺寸效应,建立了考虑这两个参数在空间-时间域对动态应力强度因子的分布进行积分后再平均来确定岩石动态断裂韧度的方法。     

白桦材断裂韧度的各向异性性质

木材可视为正交各向异性材料，表征木材抵抗裂纹扩展能力的断裂韧度硒。是木材的基本力学性质之一，它具有明显的各向异性．对白桦材试样断裂韧度硒。测试结果表明，LT试样的断裂韧度明显高于TL，TR试样的断裂韧度，TL和TR试样的断裂韧度相接近．无论哪种试样类型，起裂均发生在裂纹尖端．TL，TR试样裂纹扩展方向与原裂纹初始方向一致，LT试样与前两不同，裂纹沿着几乎平行于纤维的方向扩展．并且含水率对各个方向木材断裂韧度的影响趋势是一致的．     

一种基于SHTB的Ⅱ型动态断裂实验技术

冲击剪切载荷作用下动态断裂韧性的测定是材料力学性能和断裂行为研究中重要组成部分.为了测定材料的Ⅱ型动态断裂韧性,许多学者采用不同的试样与实验方法进行了实验,但限于实验条件,裂纹断裂模式往往是I+Ⅱ复合型,而不是纯Ⅱ型,因而不能准确测得材料的Ⅱ型动态断裂韧性.鉴于此,本文基于分离式霍普金森拉杆(split Hopkinson tension bar,SHTB)实验技术,提出一种改进的紧凑拉伸剪切(modified compact tension shear,MCTS)试样,通过夹具对MCTS试样施加约束,从而保证试样按照纯Ⅱ型模式断裂.采用实验-数值方法对MCTS试样动态加载过程进行分析,将实验测得的波形输入有限元软件ANSYS-LSDYNA,得到了裂纹尖端应力强度因子-时间曲线,并与紧凑拉伸剪切(compact tension shear,CTS)试样进行了对比.同时采用数字图像相关法进行了实验,验证了有限元分析结果.结果表明,MCTS试样在整个加载过程中K_I K_Ⅱ,裂纹没有张开;而CTS试样在同样的加载过程中K_IK_Ⅱ,出现裂纹张开现象.这说明MCTS试样能够准确地测定材料的Ⅱ型动态断裂韧性,为材料动态力学测试提供了一种有效的实验技术.     

Effect of T-stress on the mode-I fracture toughness of concrete

T-stress expressions are provided for three-point bending (TPB) beams and compact tension (CT) specimens and then its influence on mode I fracture toughness of concrete is investigated. The study shows that T-stress is dependent on the specimen's geometry and the material's property as well, and for TPB and CT specimens of regular size, T-stress is so small that its consequences can be neglected. The study also indicates that concrete specimen size should be carefully chosen to make sure the existence of K-dominance ahead of the crack tip, thus fracture toughness extracted from these specimen configurations can be reliable.     

A Shear Compression Disk Specimen with Controlled Stress Triaxiality under Quasi-Static Loading

This paper introduces a double shear axisymmetric specimen (Shear Compression Disk) and the methodology to extract flow and fracture properties of ductile materials, under various stress triaxiality levels. A thorough numerical investigation of the experimental set-up is performed, which reveals that the stresses are quite uniformly distributed in the gauge section during all the stages of the test. The attainable level of stress triaxiality (with pressures of up to 1.9 GPa) ranges from −0.1 to 1, which can be adjusted by a proper choice of geometrical parameters of the specimen. The methodology is implemented to quasi-static experiments on 4340 Steel and Aluminum 7075-T651 specimens. The flow properties are compared to those obtained by upsetting cylinders and show a very good agreement. For these materials it is observed that, contrary to the fracture strain, the flow properties are quite insensitive to the level of stress triaxiality. The fracture strain of the aluminum alloy increases with triaxiality and may be fitted with an exponential polynomial of the type suggested by [27]. These examples demonstrate the potential of the new specimen to obtain flow and fracture properties of ductile materials under controlled triaxiality.     

三维编织CMC的弯曲断裂研究

从界面断裂的角度出发，对三维编织CMC的断裂作了理论研究和数值分析，对于三点弯曲试件，通过数值拟合修正了能量释放率G的理论表达式中的自由常数A，同时也研究了材料的各个参变量对于断裂韧性的影响，由此得出了一个基本完善的三点弯曲试件断裂韧性G的理论公式，该能量释放率方法可以应用于单试件的试验计算，与断裂韧性的柔度标定方法相比，该方法一方面可以减少试验件数量；另一方面，试验结果显示出在试件切口尺雨处于0．4≤a/W≤0.5时，可以获得比较稳定的断裂韧性值。     

用短棒试件测试无烟煤的动态断裂韧度

介绍了设计的新型圆台式压头及配套的衬片加载部件,推导了采用新的加载部件进行冲击断裂实验时的断裂韧度计算公式。采用SHPB实验装置,用新加载部件对带有V形切口的无烟煤短棒试件的裂纹尖端施加拉伸载荷,测定了无烟煤的动态断裂韧度。结合准静态实验数据得到了无烟煤断裂韧度随加载率lg(dF/dt)的总体变化规律:当lg(dF/dt)6时,无烟煤的断裂韧度缓慢上升,但当lg(dF/dt)6以后,无烟煤的断裂韧度随加载率的增加快速增大。实验表明:圆台式加载比刀刃式加载更具优越性和适应性,是测试岩石类材料短棒试件动态断裂韧度较好的方法。     

Scale-dependent constitutive relations and the role of scale on nominal properties

Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a ‘background’ gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress–strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress–strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.     

厚度与加载速率对铁素体钢断裂韧性影响的SP压杆法实验研究

采用SP压杆实验方法,在常温下研究小圆薄片断裂韧性的厚度效应及加载速率对断裂特性的影响.实验结果表明,随着厚度的增加,断裂变形能增加,断裂部分的外表面因双向应力状态表现出微突起,微突起四周存在微小裂纹;随着加载速度的增加,断裂变形能增加,剪切断裂表面表现出从密集韧窝到韧窝连接成片特征.考虑试件变形过程中不同部分的能量耗散,从SP试件的整体断裂变形能得到试件的断裂韧性的宏观表达,断裂韧性随着厚度的增加而增加,随着加载速度的增加而减少.采用临界塑性断裂应变作为裂纹起裂判据,单位面积的能量耗散率作为裂纹扩展和失效判据的断裂模型,用有限元方法对SP压杆实验进行模拟,得到与实验结果比较相符的模拟结果.     

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.