T应力对Ⅰ-Ⅱ复合型裂纹扩展的影响

利用最大周向正应力判据MTS重新分析研究了脆性破坏的Ⅰ-Ⅱ复合型裂纹扩展,其中考虑了平行于裂纹方向的非奇异项T应力。以平板中的斜裂纹处于双向受力为研究对象,通过两个方向力的不同组合以及裂纹与受力方向的夹角变换得到包括纯I型和纯II型在内的Ⅰ-Ⅱ复合型裂纹,分析了T应力对裂纹扩展方向以及断裂时的应力强度因子的影响,并将预测结果与现有的实验数据进行了比较。在此基础上,给出了不同T应力条件下通用的Ⅰ-Ⅱ复合型裂纹扩展条件,可用于给定几何试件的脆性断裂判定。分析结果表明:裂纹尖端非奇异项T应力对裂纹扩展的影响是不可忽略的,尤其是对II型断裂的影响更为明显。     

Effect of non-singular stress on the brittle fracture of V-notched structure

The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.     

Significance of K-dominance zone size and nonsingular stress field in brittle fracture

Stress intensity factor has been used to characterize the fracture toughness of a brittle material. This practice is apparently based on the assumption that the singular stress alone at the crack tip is responsible for fracture and that the nonsingular part of the near tip stress has no effect on fracture. In this study, mode I fracture experiments were conducted on a brittle material (PMMA) with four different specimen configurations. The result indicated that fracture toughness cannot be described by stress intensity alone and that a second parameter representing the influence of the nonsingular stress is needed. A two-parameter fracture model was proposed and validated with the experimental result. This two-parameter model was shown to be able to account for various effects created by specimen configurations, crack sizes, and loading conditions, on the fracture behavior of brittle materials.     

Effects of residual stress on toughening of brittle polycrystals

The effects of residual stress on toughening of brittle polycrystalline materials, in the absence of microcracking, were investigated by considering the mode I stress intensity factor reduction at the tip of a stationary crack under combined applied and residual stress loading. Toughness enhancement associated with a number of model singular and non-singular residual stress fields was evaluated. The singular residual stress fields were used to model grain-sized thermal expansion anisotropy due to grain-orientation differences in a polycrystal. The numerical results indicate that residual stress can significantly toughen a stationary crack against initiation. For the same average value of residual stress, toughness enhancement due to singular residual stress fields is more substantial than that due to non-singular residual stress fields. Sample toughness enhancement results are presented for a single-phase polycrystal failing by intergranular fracture.     

FATIGUE CRACK PROPAGATION IN BIAXIAL STRESS FIELDS

Abstract Biaxial tension-compression fatigue tests were conducted with cruciform shaped specimens in a closed-loop servo hydraulic testing machine. The effects of static and cyclic non-singular stresses acting parallel to the crack plane on the crack growth rate are discussed based on the experimental observations of crack opening behaviour and fractography. Those non-singular stresses did affect the growth rate significantly under certain conditions. The range of crack-tip opening displacement was found to be a better parameter in correlating the growth rate than the stress intensity range or its effective range. The rate tended to increase with increasing non-singular stress which is correlated to the opening displacement range. This tendency was explained by the shift of fracture mechanisms to a more brittle type due to a higher elevation of hydrostatic stress near the crack tip for the case of a larger non-singular stress term.     

Loading Rates and the Dynamic Initiation Toughness in Brittle Solids

The experimentally determined marked rise of the stress intensity factor required to initiate crack propagation in brittle solids under variably high loading rates, is analyzed. This problem of fracture initiation at the tip of a crack is considered in terms of activating a flaw at some distance away from the tip. By using a semi-infinite crack in an unbounded two-dimensional solid subjected to spatially uniform but temporally varying crack-face pressure, we consider the evolution of stress at the failure initiation site. Fracture initiation is assumed synonymous with attaining a critical stress at the fracture site. The results conform to typical experimental data of dynamic crack initiation in brittle solids.     

FATIGUE CRACK GROWTH LAWS FOR BRITTLE AND DUCTILE MATERIALS INCLUDING THE EFFECTS OF STATIC MODES AND ELASTIC-PLASTIC DEFORMATION

A fatigue crack growth damage accumulation model is used to derive laws for the fatigue crack growth rates of brittle and ductile materials. The damage accumulated during cyclic loading is assumed to be proportional to the cyclic change in the plastic displacement in the crack tip yielded zone. The static mode contribution to the fatigue damage is assumed to be proportional to some power of the crack tip displacement. The laws are applicable in either the small or large scale yielding regimes provided that the stress ratio remains positive. Static modes are assumed to be controlled by the fracture toughness value in brittle materials, and by the gradient of the crack growth resistance curve in ductile materials. In the analysis of ductile materials it is assumed that the crack growth resistance of the material is not significantly altered by fatigue crack growth.
The growth rate equations are expressed in terms of the near field value of the J -integral, i.e. the value which would be calculated from assuming the material deformed in a non-linear elastic manner during the increasing load part of the fatigue cycle. Examples are given of the predictions of the growth law for ductile materials. It is predicted that after the initiation of stable tearing the crack growth rate, when expressed in terms of the cyclic change in the stress intensity factor, depends on both the structural geometry and the degree of crack tip plastic deformation. In both brittle and ductile materials the fatigue crack growth rate is predicted to accelerate as the failure criteria relevant to static crack instability are approached.     

Evaluation of dynamic fracture toughness parameters of locomotive axle steel by instrumented Charpy impact test

The analysis of the energy of fracture of specimens from steel OSL, which is widely used for the manufacture of railway axles under shock loading, is performed. The nature and quantitative parameters of the typical stages of the processes of plastic and brittle fracture, depending on the test temperature and stiffness of the stress state at the tip of the crack‐like defect, are established. It is shown that impact loading at 20 °C leads to the formation of the local zone of plasticity and ductile–brittle fracture of the material. An increased stiffness of the stress state at the tip of the defect at ?40 °C causes brittle fracture. An approach is developed, which is based on using the size of shear lips as a quantitative parameter of fracture under normal and low temperatures, similar in its physical essence to deformation approaches of nonlinear fracture mechanics. Based on this approach and the quantitative analysis of specimen fracture zones, the physical and mechanical scheme of specimen fracture is proposed in the presence of localized plasticity and in its absence near the tip of the concentrator.     

On T-Stresses Near V-Notches

The second term of stress field around a sharp V-notch under mode I loading was investigated. It was found that in the Cartesian coordinate system, unlike the T-stress in cracked bodies, the second term of Williams’ expansion in all three stress components is nonzero and its value depends on the distance from the notch tip. Thus, according to the stress based fracture criteria, in addition to the singular term, the first non-singular term may also play an important role in brittle fracture of sharp V-notched components under mode I loading.     

Mode I cracks subjected to large T-stresses

There are several criteria for predicting brittle fracture in mode I and mixed mode loading. In this paper, the modified maximum tangential stress criterion originally proposed for mixed mode loading, is employed to study theoretically brittle fracture for mode I cracks. In particular, the effect of the non-singular term of stress, often known as the T-stress, on the angle of initiation of fracture and the onset of crack growth is explored. The T-stress component of the tangential stress vanishes along the crack line. Therefore, it is often postulated for linear elastic materials that the effect of T-stress on mode I brittle fracture can be ignored. However, it is shown here that the maximum tangential stress is no longer along the line of initial crack when the T-stress exceeds a critical value. Thus, a deviation in the angle of initiation of fracture can be expected for specimens having a large T-stress. It is shown that the deviation angle increases for larger values of T-stress. Theoretical results show that the apparent fracture toughness decreases significantly when a deviation in angle occurs. Earlier experimental results are used to corroborate the findings. The effect of large T-stresses is also explored for a crack specimen undergoing moderate scale yielding. The elastic-plastic investigation is conducted using finite element analysis. The finite element results reveal a similar deviation in the angle of maximum tangential stress for small to moderate scale yielding.     

Analytical stress intensity solution for the stable Poisson loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-curve determination. The crack mouth opening displacements (CMOD's) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMOD's, and crack displacement profiles, are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials.     

Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

A coupled model resulting from the boundary element method and eigen‐analysis is proposed in this paper to analyse the stress field at crack tip. This new combine method can yield several terms of the non‐singular stress in the Williams asymptotic expansion. Then the maximum circumferential stress (MCS) criterion taken the non‐singular stress into account is introduced to predict the brittle fracture of cracked structures. Two earlier experiments are re‐examined by the present numerical method and the role of the non‐singular stress in the brittle fracture is investigated. Results show that if more terms of non‐singular stress are taken into account, the predicted crack propagation direction and the critical loading by MCS criterion are much closer to the existing experimental results, especially for dominating mode II loading conditions. Moreover, numerical results manifest that Williams series expansion can describe the stress field further from the crack tip if more non‐singular stress terms are adopted.     

STRESS-RATIO EFFECT OF FATIGUE CRACK PROPAGATION IN A BIAXIAL STRESS FIELD

Fatigue crack propagation tests were conducted under conditions of equibiaxial, uniaxial and shear loading by using a cruciform specimen in a servo hydraulic testing machine. The effect of non-singular stress cycling on the fatigue crack propagation rate was examined based on the observation of crack opening behavior. The crack propagation rate was significantly influenced by the non-singular stress parallel to the crack when it was correlated to the stress intensity range. The crack closure behavior was greatly affected by the non-singular stress. The crack propagation rate was uniquely correlated to the effective range of the stress intensity factor except for the case of completely reversed shear loading where significant plasticity was detected. The crack opening displacement range was concluded to be a parameter controlling the crack propagation rate for all the stress conditions examined in the present experiments. Some discussion is made on the effect of material anisotropy on fatigue crack propagation in a biaxial stress field.     

Fracture toughness of 2-D carbon fibre reinforced carbon composites

The fracture toughness of 2-D woven carbon fibre reinforced carbon laminate has been evaluated by linear elastic fracture mechanics (LEFM),R-curve andJ-integral analysis using the single edge-notched bending (SENB) specimen of edge and flatwise geometries. The edgewise specimens failed by a small extension of the self similar crack whereas the flatwise specimens failed by delamination. The surface damage developing from the tip of the initial crack was revealed by the brittle lacquer coating technique and the zone shape varied with the specimen geometry, i.e. the loading axis relative to the woven layers. Acoustic emission (AE) was also used to monitor crack growth, and the total ring down count of AE was observed to increase as the initial crack length was decreased. Both the damage zone size and total AE counts were found to increase in two linear stages as a function of the square of the stress intensity factor,K.     

Limitations on the use of the mixed-mode delaminating beam test specimen: Effects of the size of the region of K-dominance

The mixed-mode delaminating beam (MMDB) is a widely used test geometry designed to measure the fracture resistance of bimaterial interfaces under mixed-mode loading conditions. In the present work, linear-elastic finite element analyses are employed to determine the complex stress intensity factor, K, for an interfacial crack in this sample; results are found to confirm those of previous studies of the bilayer specimen. However, the numerical results further reveal that the region of K-dominance near the crack tip is very limited, extending merely 1/100 to 1/1000 of the sample height, about an order of magnitude smaller than for other common fracture-mechanics test samples. Analyses performed for this specimen geometry modified to include a thin sandwiched interlayer also indicate a very limited region of K-dominance, for example, extending 1/10 of the height of the sandwiched layer from the crack tip for very thin sandwiched layers. For the sandwiched geometry, two situations leading to a useful small scale yielding condition are described. Examples of the use of this specimen in the evaluation of the fracture toughness of ceramic joints are cited from the literature and comparisons are made between the size of the K-dominant region and the extent of crack tip plasticity. Based on these comparisons, the geometry-independent predictive power of linear-elastic fracture mechanics for common bimaterial couples and specimen dimensions using this geometry is challenged.     

Dynamic crack initiation toughness of 4340 steel at constant loading rates

Determination of fracture toughness for metals under quasi-static loading conditions can follow well-established procedures and ASTM standards. The use of metallic materials in impact related applications requires the determination of dynamic crack initiation toughness for these materials. There are two main challenges in experiment design that must be overcome before valid dynamic data can be obtained. Dynamic equilibrium over the entire specimen needs to be approximately achieved to relate the crack tip loading state to the far-field loading conditions, and the loading rate at the crack tip should be maintained near constant during an experiment to delineate rate effects on the values of dynamic crack initiation toughness. A recently developed experimental technique for determining dynamic crack initiation toughness of brittle materials has been adapted to measure the dynamic crack initiation toughness of high-strength steel alloys. A Kolsky pressure bar is used to apply the dynamic loading. A pulse shaper is used to achieve constant loading rate at the crack tip and dynamic equilibrium across the specimen. A four-point bending configuration is used at the gage section of the setup. Results are presented which show a monotonically increasing rate dependence of crack initiation toughness for 4340 high-strength steel.     

Creep crack growth modeling and near tip stress fields

The problem of near tip stress fields in a cracked body subjected to Mode I loading at elevated temperatures is studied. Specifically, the superalloy, IN 718, is examined in the standard compact tension specimen geometry. The simulation is at 650°C. The specimen is assumed to be under dead load conditions. For a stationary crack, the near tip stress fields are calculated and compared with the asymptotic solutions available in the literature. While the results assuming small strains agree very well with the asymptotic solutions, the large strain analysis does not. The results indicate that both the amplitude and the asymptotic exponent are dependent on the applied load level which is in disagreement with the asymptotic predictions. In addition, the zone effected by creep deformation is larger when large strains are considered. An algorithm is developed and tested for the modeling of stable crack growth. Both convergence and stability are investigated. Explicit time integration is used for crack growth studies as it is demonstrated to be computationally more efficient. The algorithm is employed to study the near tip stress fields for a growing crack. The near tip stress fields for a growing crack (with constant velocity) are generated using the developed algorithm. The results demonstrate that the asymptotic behavior of the stress field is load dependent. Comparison is made with the limited analyses available. Recommendations for future research are discussed.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Characterization of crack tip stress fields in test specimens using mode mixity parameters

The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the $T$ -stress, elastic–plastic stress fields, integration constant $I_{n}$ , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field $I_{n}$ and the $T$ -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the $T$ -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.     

On the Presence of the Out–of–Plane Singular Mode Induced by Plane Loading With K<Subscript>II</Subscript> = K<Subscript>I</Subscript> = 0

Previous studies by a number of researchers demonstrated that in the case of a plane crack subjected to shear loading conditions characterized by a remote stress intensity factor, K_II, a three-dimensional singular mode (called mode O or out-of-plane mode) develops at the crack tip. This singular mode occurs due to the primary shear loading and Poisson’s effect. Similar to mode III, the O-mode is associated with the transverse shear stress components. Recent theoretical and numerical studies have also demonstrated a strong presence of this singular mode in plates weakened by pointed V-notches. Therefore, it was suggested that O-mode can play an important role in fracture initiation, particularly at large opening angles (above 102.6°) when the applied mode II is non-singular.