Using torsional bar testing to determine fracture toughness

A new method to determine fracture toughness K _IC of materials is introduced. A round-rod specimen having a V-grooved spiral line with a 45° pitch is tested under pure torsion. An equibiaxial tensile/compressive stress state is effectively created to simulate conventional test methods using a compact-type specimen with a thickness equivalent to the full length of the spiral line. K _IC values are estimated from the fracture load and crack length with the aid of a three-dimensional finite element analysis. K _IC of 7475-T7351 aluminium is estimated to be 51.3 MPa √m, which is higher than the vendor's value in the TL orientation by ∼0.8% and higher than 0.5T compact tension (CT) value by 6%; A302B steel yields 54.9 MPa √m being higher than CT test value by ∼2%. Good agreement between the K _IC values obtained by different methods indicates the proposed method is sound and reliable.     

An approach to size effect in fatigue of metals using fractal theories

ABSTRACT As was experimentally observed by several authors, the fatigue strength of metallic materials decreases with increasing the specimen size. Such a decrease can be remarkable for very large structures like, for example, big cargo ships (some hundred meters long) transporting oil or other goods. Size effect in fatigue is herein explained by considering the fractal nature of the reacting cross sections of structures, that is, the renormalized fatigue strength is represented by a force amplitude acting on a surface with a fractal dimension lower than 2, where such a dimensional decrement depends on a self‐similar weakening of the material ligament, owing to the presence of cracks, defects, voids and so forth (microscopic level). However, this decrement tends to progressively disappear with increasing the structure size (macroscopic level), i.e. the effect of the material microstructure on the macroscopic fatigue behaviour gradually vanishes for structures large enough with respect to a characteristic microstructural size, this phenomenon being defined as multifractality. A multifractal scaling law for fatigue limit of metals is proposed, and some experimental results are examined in order to show how to apply the theoretical approach presented.     

A modified specimen for evaluating the mixed mode fracture toughness of adhesives

This article introduces a specimen geometry that allows the separation of fracture energy release rates G _I and G _II in adhesively joined beams made of disparate materials. The analysis is based upon a Green's functions formulation for shear deformable beams and circumvents the need to employ finite element computations. The current method results in a system of non-singular integral equations, that can be discretized and reduced to a system of algebraic equations which may be solved by common numerical techniques. The analysis accounts for the dimensions and properties of the adhesive and provides results for a wide range of G _I, G _II and their ratio. Those results agree with finite element computational values to within less than 4%.     

An investigation on the effects of equal channel angular pressing on the mixed‐mode fracture toughness and mechanical properties of 6063 aluminium alloy

In this study, effects of equal channel angular pressing (ECAP) on the mixed‐mode fracture toughness of Al‐6063 were investigated. The ECAP process continued up to 5 passes without failure. Grain refinement was obvious after 5 passes of the ECAP process. The average grain size reduced from 45μm to less than 1μm, and textural studies shows aligning the grains in known directions. After 4 passes, yield and ultimate strengths increase respectively from 100 and 209 MPa to 300 and 375 MPa and reduction in elongation was also observed. The microhardness improved after the process. The fracture toughness for different orientations was measured. For pure mode I (opening mode), its value decreased after the first pass from 18.4 to 15.71  ; however, it increased to about 18.8  after the fifth pass. For mixed‐mode loading condition, different orientations were investigated. The results revealed different fracture toughness reductions after the first passes of the process for specimens with different orientations. The fracture surfaces were studied by using scanning electron microscope, and refined equiaxed dimples were observed after the ECAP process.     

Self-affinity of fracture surfaces and implications on a possible size effect on fracture energy

As demonstrated within the last 15 years by numerous experimental studies, tensile fracture surfaces exhibit a self-affine fractal geometry in many different materials and loading conditions. In the last few years, some authors proposed to explain an observed size effect on fracture energy by this fractality. However, because they did not consider a lower bound to this scale invariance (which necessarily exists, at least at the atomic scale), they had to introduce a new definition of fracture energy with unconventional physical dimensions. Moreover, they were unable to reproduce the observed asymptotic behavior of the apparent fracture energy at large specimen sizes. Here, we show that this is because they considered self-similar fracture surfaces (not observed in nature) instead of self-affine. It is demonstrated that the ignorance of the self-affine roughness of fracture surfaces when estimating the fracture energy from the work spent to crack a specimen necessarily leads, if the work of fracture is proportional to the fracture area created, to a size effect on this fracture energy. Because of the self-affine (instead of self-similar) character of fracture surfaces, this size effect follows an asymptotic behavior towards large scales. It is therefore rather limited and not likely detectable for relatively large sample sizes (10^–1 m). Consequently, significant and rapid increases of the apparent fracture energy are more likely to be explained mainly by other sources of size effect.     

The effect of basalt fibres on fracture toughness of asphalt mixture

This paper deals with the effect of basalt fibres on fracture toughness of asphalt mixture. For this purpose, basalt fibres with three different contents (i.e., 0.1%, 0.2%, and 0.3% by weight of asphalt mixture) and lengths (ie, 4, 8, and 12 mm) are incorporated into asphalt mixture to prepare fibre‐reinforced asphalt mixtures. Fracture tests are then carried out on these mixtures under four different modes of loading (i.e., pure mode I, pure mode II, and two mixed modes of I/II) using semicircular bend (SCB) specimens. The results exhibit that the fracture toughness increases with the enhancement of the fibre content. In addition, increase in the length of basalt fibre results in reduction of the fracture toughness of asphalt mixture. However, the asphalt mixture containing 0.3% of basalt fibres with the length of 4 mm shows the highest fracture toughness compared with other mixtures. It is also found that the basalt fibre improves mode I fracture toughness of asphalt mixtures more significantly than mode II one. Statistical analysis is also performed on the experimental data. Analysis of ANOVA demonstrates that all the three factors investigated in this study (i.e., length of basalt fibre, content of basalt fibre, and mode of loading) have significant influence on the fracture toughness of asphalt mixtures.     

Mixed-mode I/II fracture behaviour of a high strength steel

Mixed mode fracture in a certain high strength steel has been investigated through physical experiments and numerical calculations. The main objective has been to investigate the implications of local crack tip processes on the macroscopic mixed mode fracture behaviour. A scrutiny of the fractured specimens revealed evidence of crack branching in all cases where β_{_eq} < 40° ( β_{_eq =} atan ( K_{_I} /K_{_II} ) ). The appearance of branching was found to be accompanied to a rather abrupt increase in the macroscopic mixed mode fracture toughness. In the numerical calculations the effective plastic strain criterion suggested by Hallbäck and Nilsson (1994) was applied to the present material. Crack tip branching was from the analysis predicted to occur at β_{_eq =} 60°. Besides the presence of branching, it was however questionable whether the analysis corroborated the experimentally observed behaviour.     

An insight into mode II fracture toughness testing using SCB specimen

The effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors K_I and K_II but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.     

脆性材料微裂缝无序度与尺寸效应

假定在某些脆性无序材料内含有相同的微裂缝随机分布概率密度,但具有不同无序度的情况下,建立了模拟材料力学行为的二维不连续位移法边界元数值计算模型.实现了材料微裂缝生长、扩展到最终破坏的全过程数值仿真.根据分形几何理论确定了材料断裂表面几何形貌的分形维数.得到了材料的断裂强度随微裂缝长度随机分布无序度的增加而降低的规律性.数值模拟结果符合Bazant尺寸效应定律,并进一步证实了脆性或准脆性无序材料产生尺寸效应的微观机理.     

The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading

The purpose of this paper is to revisit the maximum tensile stress (MTS) criterion to predict brittle fracture for mixed mode conditions. Earlier experimental results for brittle fracture of polymethylmethacrylate (PMMA) using angled cracked plates are also re-examined. The role of the T -stress in brittle fracture for linear elastic materials is emphasized. The generalized MTS criterion is described in terms of mode I and II stress intensity factors, K _I and K _II and the T- stress (the stress parallel to the crack), and a fracture process zone, r _c . The generalized MTS criterion is then compared with the earlier experimental results for PMMA subjected to mixed mode conditions. It is shown that brittle fracture can be controlled by a combination of singular stresses (characterized by K ) or non-singular stress ( T -stress). The T -stress is also shown to have an influence on brittle fracture when the singular stress field is a result of mode II loading.     

A new fixture for fracture tests under mixed mode I/II/III loading

In this paper, a new loading device for general mixed mode I/II/III fracture tests is designed and recommended. Finite element analyses are conducted on the proposed apparatus to evaluate the fracture parameters of the tested samples under various mixed mode loading conditions. The numerical results revealed that the designed loading fixture can generate wide varieties of mode mixities from pure tensile mode to pure in‐plane and out‐of‐plane shear modes. The accuracy of the proposed fixture is evaluated by conducting a wide range of fracture tests on compact tension shear (CTS) specimens made of polymethyl methacrylate (PMMA). The experimental results are then compared with the theoretical predictions obtained by the Richard criterion. A good consistency is observed between the experimental results and theoretical predictions.     

Weight Function for an Inclined Edge Crack in a Semiplane

The matrix-like structure of the Weight Function (WF) for determining the Stress Intensity Factors (SIFs) in a nonsymmetric plane body is obtained from the general properties of the elastic field. General asymptotic and symmetric properties of the WF are discussed. By extending a previously proposed methodology, an analytical approximate WF is determined for an edge crack in a semiplane within the range of inclination (-75^–75^). Finite Element evaluations considering the minimum number of loading conditions were performed to this purpose. The accuracy of the SIFs obtained by the WF is found in the order of a few tenths of percent. The solution of a typical problem illustrates the practical usefulness of the WF. This revised version was published online in July 2006 with corrections to the Cover Date.     

无序材料微裂缝分形几何与尺寸效应的微观机理

针对一些含有相同的微裂缝随机分布概率密度但无序度不同的材料,建立了模拟材料断裂力学行为的二维不连续位移法边界元数值计算模型,实现了材料微裂缝的生长、扩展到最终破坏的全过程数值模拟.从分形几何的新视角深入地揭示了脆性或准脆性无序材料产生尺寸效应的微观机理.材料断裂力学行为的数值模拟结果与Bazant尺寸效应定律相符,不仅与微缺陷的密度有关,更与微缺陷大小随机分布的无序度相关,无序度越大的材料其尺寸效应越明显.得到了用初始分形维数D0表示的关于材料断裂强度的分形维数Dσ经验公式,可以更深入地解释材料的微观尺寸效应机理和断裂过程.     

Quantification of constraint effects in fracture mechanism transition for cracked structures under mixed mode loading

The objective of the study is to evaluate the effects of plastic constraint on transition between tensile-type and shear-type fracture. The T -stress is employed as the quantifying parameter for constraint and is incorporated into the existing theoretical criteria for modelling this transition. It is found that different constraint levels can dramatically alter the transition point. To verify this finding, two sets of mixed mode tests with different constraint levels are carried out. Alongside the theoretical and experimental study, finite element simulation is performed to verify and support these findings. Substantially improved agreement is observed with experimental data if the effect of plastic constraint on transition is included.     

Survey on fatigue strength of cast bronzes intended for marine propellers

The proper characterization of cast materials is rather challenging because of wide deviations of material features due to the fabrication process. In the frame of propeller design, a recently proposed fatigue assessment procedure highlighted the need of reliable fatigue strength characterization of cast bronzes. With the aim of obtaining reference S–N curves to support the fatigue assessment of propeller blades and to evaluate the effect on fatigue strength of the most influencing parameters, a comprehensive literature survey was carried out. It appeared that fatigue strength of cast bronzes is quite challenging to evaluate, firstly, because the properties may considerably differ from small specimens to real blades and, secondly, because relatively few experimental data are openly available.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

Size effect and inverse analysis in concrete fracture

This paper summarizes the basic experimental and numerical results supporting an easy procedure to determine up to two fracture parameters based on numerically computed size effect curves. Furthermore, it supplies closed-form expressions to determine the initial linear segment approximation of the (stress vs. crack opening) softening curve of cohesive crack models for concrete, based only on the peak loads determined in splitting-tension (Brazilian) tests and in three-point-bending test on notched specimens. Knowledge of the initial segment, although not enough to describe all the fracture process of concrete structures, is enough to predict the fracture behavior of unnotched concrete structures prior and around the peak load. The same is true for notched structures provided their size is less than a limiting size, approximately defined in the paper. This revised version was published online in July 2006 with corrections to the Cover Date.     

An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete*

An embedded cohesive crack model is proposed for the analysis of the mixed mode fracture of concrete in the framework of the Finite Element Method. Different models, based on the strong discontinuity approach, have been proposed in the last decade to simulate the fracture of concrete and other quasi‐brittle materials. This paper presents a simple embedded crack model based on the cohesive crack approach. The predominant local mode I crack growth of the cohesive materials is utilized and the cohesive softening curve (stress vs. crack opening) is implemented by means of a central force traction vector. The model only requires the elastic constants and the mode I softening curve. The need for a tracking algorithm is avoided using a consistent procedure for the selection of the separated nodes. Numerical simulations of well‐known experiments are presented to show the ability of the proposed model to simulate the mixed mode fracture of concrete.     

An adaptive finite element framework for fatigue crack propagation

A new finite element (FE) framework for fatigue crack propagation (FCP) analysis is proposed. This framework combines the simplicity of standard industrial FCP analysis with the generality and accuracy of a full FE analysis and can be implemented on a small computer by combining standard existing computational tools. In this way it constitutes an attractive alternative to existing approaches. The framework is based on linear elastic fracture mechanics and on FE mesh adaptation. Some novel features are introduced in several of its steps in order to make it efficient and at the same time reasonably accurate. Various computational aspects of the scheme are discussed. A few two‐dimensional numerical examples involving FCP in thin sheets under plane‐stress conditions are presented to demonstrate the performance of the framework. Some of the numerical results are compared to those of laboratory experiments. Copyright © 2002 John Wiley & Sons, Ltd.     

Two parameter approach for elastic-plastic fracture of short cracked specimens under mixed mode loading

For mode-I loading, in order to describe the near-tip stress field in a specimen under large scaled yielding, two parameter approaches such as J-T, J-Q and J-A₂ theories have been developed and proved well for their validity and limit. In this work elastic-plastic finite element analysis were performed to investigate the effects of mode mixity and T-stress upon near-tip stress distribution for a small-scale-yield model with the modified boundary layer and CTS (Compact Tension-Shear) configuration under large-scale-yield state. As the results, some peculiar characteristics were found as follows; As the mode mixity increases, normal stresses _rr and near the crack tip in the small-scale-yield model get significantly affected by the positive T-stress as well as the negative T-stress, while the shear stress _r is little affected by T-stress. Also, the near-tip stress distribution of short cracked CTS specimens under the large-scale-yield state agree fairly well with that of the small-scale-yield model with an appropriate positive T-stress. The two parameters approach with J-integral and T-stress seems to be a good tool for describing the near-tip stress field under a mixed mode loading and large-scale-yield state.