Simple method to measure the crack resistance of ceramic materials

A new and simple method to study the change in crack resistance during the process of crack growth in ceramic materials has been developed. The method is based on using the chevron-notched short-bar test which is generally accepted as a convenient method for measuring fracture toughness. The simple modification described here allows one to measure fracture toughness using the assumption that fracture toughness changes in the process of crack growth (presence of crack resistance curve, or R-curve). This method presents many advantages, especially the long stable crack growth under mode I fracture specimen and plane strain, small specimen size and no need of pre-cracking for measuring R-curve behaviour in ceramic materials.     

纯Ⅰ型加载条件下有机玻璃中心切口圆盘断裂的尺寸相关性

采用直槽式和尖槽式中心切口圆盘试件,对有机玻璃在纯Ⅰ型准静态加载条件下的断裂行为进行了实验研究.结果表明,中心切口圆盘试件的切口形状对断裂行为和断裂韧度的测试结果有显著的影响.直槽切口偏离理想裂纹,裂纹起裂始于切口端部的角点,实测的断裂韧度值偏高且具有尺寸相关性;尖槽切口接近理想裂纹,裂纹起裂始于尖角的顶点,实测的断裂韧度不存在尺寸相关性,即是材料常数.     

Dynamic fracture mechanics—A scientific tool for the prevention of catastrophic failure

The major area of research in dynamic fracture has been the extension of the concept of static fracture toughness to predict crack arrest for a propagating crack. In this work crack propagation due to a ductile (microvoid) mechanism and cleavage (brittle) mechanism, as well as transition from one mode to another, has been analysed theoretically. Dynamic fracture toughness as a function of crack velocity has been determined. Temperature distribution near a propagating crack tip has been predicted for plane stress condition. The effect of reflected stress wave in a single edge notch specimen under transient crack growth conditions has also been analysed.     

Numerical analysis of the ENF and ELS tests applied to mode II fracture characterization of cortical bone tissue

The objective of this work is to verify numerically the adequacy of the ENF and the ELS tests to determine the fracture toughness under mode II loading of cortical bovine bone tissue. A data‐reduction scheme based on the specimen compliance and the equivalent crack concept is proposed to overcome the difficulties inherent to crack monitoring during its growth. A cohesive damage model was used to simulate damage initiation and growth, thus assessing the efficacy of the proposed data‐reduction scheme. The influences of the initial crack length, local strength and toughness on the measured fracture energy were analysed, taking into account the specimen length restriction. Some limitations related to spurious influence on the fracture process zone of the central loading in the ENF test, and clamping conditions in the ELS test were identified. However, it was verified that a judicious selection of the geometry allows, in both cases, a rigorous estimation of bone toughness in mode II.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Study of mode I crack dynamic propagation behaviour and rock dynamic fracture toughness by using SCT specimens

To study crack dynamic propagation behaviour and rock dynamic fracture toughness, a single cleavage triangle (SCT) specimen was proposed in this paper. By using these specimens and a drop‐weight test system, impact experiments were conducted, and the crack propagation velocity and the fracture time were measured by using crack propagation gauges. To examine the effectiveness of the SCT specimen and to predict the test results, finite difference numerical models were established by using AUTODYN code, and the simulation results showed that the crack propagation path agrees with the test results, and crack arrest phenomena could happen. Meanwhile, by using these numerical models, the crack dynamic propagation mechanism was investigated. Finite element code ABAQUS was applied in the calculation of crack dynamic stress intensity factors (SIFs) based on specimen dimension and the loading curves measured, and the curves of crack dynamic SIFs versus time were obtained. The fracture toughness (including initiation toughness and propagation toughness) was determined according to the fracture time and crack speeds measured by crack propagation gauges. The results show that the SCT specimen is applicable to the study of crack dynamic propagation behaviour and fracture toughness, and in the process of crack propagation, the propagation toughness decreases with crack propagation velocity, and the crack arrest phenomena could happen. The critical SIF of an arrest crack (or arrest toughness) was higher than the crack propagation toughness but was lower than the initiation toughness.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

A three-point bend specimen with partly tapered cross-section sides

The stress intensity factor and the J-integral have been derived analytically and numerically for a modified three-point bend specimen with partly tapered sides, for various crack lengths, taper and specimen cross-section proportions, in order to allow full-thickness testing of tapered samples, common in older steel structures, to obtain a fair effective fracture toughness value for a through thickness crack in inhomogeneous materials. The stress intensity factor is obtained with the approximate analytical method of Kienzler and Herrmann, based on the concept of material forces. The J-integral is calculated numerically with a 3D finite element model for a linear elastic material and an elastic ideal-plastic material. A simple single specimen fracture toughness evaluation procedure is proposed. It is found that the effect of taper in the range encountered in practice is small, of the order of a few percent.     

Der Mischbruch im Zugversuch

Mixed fracture in the tension test If a tensile test specimen does not break before by cleavage, voids are nucleated at second-phase particles and inclusions during plastic deformation. At the center of the necked region these voids coalesce by internal necking or shearing of the material between them forming a fibrous crack which expands radially. In a temperature range which is dependent on the material cleavage fracture is initiated by the fibrous crack, resulting in a mixed fracture. If no cleavage fracture is initiated a completely fibrous fracture is formed. Mixed fracture surfaces consist of a cleavage fracture zone surrounding the central fibrous fracture zone and the tensile specimen behaves like a fracture mechanics specimen. Fracture toughness can be calculated by equations for tensile specimens with a central penny shaped crack. A comparison of fracture toughness values obtained by the use of unnotched tensile specimens and of fracture mechanics specimens show good agreement inbetween the temperature range of valid K_lc values according to standards of linear-elastic fracture mechanics.     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

UNSTABLE FATIGUE CRACK PROPAGATION AND FATIGUE FRACTURE TOUGHNESS OF STEELS

This paper presents the results of fatigue crack growth and fatigue fracture toughness studies of a high-pressure vessel steel with particular emphasis on the influence of heat treatment, low temperatures, plastic prestraining, the stress ratio and specimen dimensions. It has been shown that steels in an embrittled state, caused primarily by thermal treatment and low-temperatures, exhibit unstable fatigue crack growth which is characterized by alternate crack jumps (cleavage zones) and zones of fatigue crack growth. The fatigue fracture toughness, which corresponds to the first crack jump, and final fracture can be appreciably lower (i.e. up to 50%) than the static fracture toughness under plane strain conditions at the corresponding temperature. An analysis has been performed of unstable and stable fatigue crack growth and a model of unstable crack propagation is proposed which accounts for the observed experimental behaviour.     

The effect of initial notch shape of compact specimen on fatigue pre-cracking and fracture toughness testing

The circular notched compact specimens, along with standard specimens having straight or chevron notch are provided for fatigue and fracture toughness testings in order to study the crack observation capability during fatigue pre-cracking, skewness of the crack front, and the resulting fracture toughness K_Q. The test results indicated that circular notched specimens significantly facilitate the crack observation during fatigue testing as the cracks initiate on both surfaces of the specimen. No remarkable differences were observed on geometries of the fatigue crack front obtained and the resulting fracture toughness among these three types of specimen. The macroscopic observation of beach marks on the fracture surfaces revealed that, in the present material Ti-6Al-4V (ELI), the advance of only 1.3% of the whole crack length corresponded to the load level at which fracture toughness K_Q was evaluated.     

Bruchmechanische Eigenschaften von metastabilen Austeniten

Fracture Mechanical Properties of Metastable Austenites The effect of a martensitic tranformation at the crack tip on fracture mechanical properties was investigated with FeNiAl-model alloys. Transformable austenite and martensite obtained by deep-cooling showed a completely different behaviour. The martensite has high yield stress, normal dependence of fracture toughness of specimen diameter, and a low threshold for the start of fatigue crack growth. Characteristic for the metastable austenite is a high work hardening ability (at a low yield stress) by stress-induced martensitic transformation in a zone at the crack tip, which is surrounded by untransformed austenite. This leads to a compressive internal stress, which impedes crack growth. A consequence is a high fracture toughness, which even increases with specimen thickness, and a very high threshold value for fatigue crack growth. Localized stress induced martensitic transformation associated with a positiv volume change can explain the anomalous fracture mechanical properties of the alloys in the metastable austenitic state.     

Fracture toughness measurement by cylindrical specimen with ring-shaped crack

A method for measuring the plane strain fracture toughness of metals by means of cylindrical specimen in tension with axi-symmetrical ring-shaped crack is discussed. Owing to the fact that the crack tip of such a specimen is closer to ideal plane strain state, the K_1c value measured is effective and reliable. This investigation has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen dimensions.In both safety evaluation and life estimation of engineering components by linear elastic fracture mechanics, it is necessary to measure the fracture resisting parameter—fracture toughness under plane strain. According to the ASTM-E399-74 standard[1], when measuring the fracture toughness K_1c values of medium and low strength steels with a standard compact tension specimen or three-point bending specimen, it is necessary to use specimens of large dimensions, great tonnage fatigue testing machine and universal testing mechine. Naturally, this presents great difficulties to the investigation and application of fracture mechanics and it is precisely for the purpose of overcoming these difficulties that we have studied the method of measuring the plane strain fracture toughness by a cylindrical specimen in tension with axi-symmetrical ring-shaped crack. This method has fairly satisfactorily solved the problems of crack prefabrication, experimental technique, data processing and requirements for specimen size. Owing to the fact that the field around the crack tip of such a specimen is closer to ideal plane strain state, the results obtained are values smaller than those by using compact tension and three-point bending specimens and are more reliable fracture resisting constants for materials in linear elastic fracture mechanics analysis. Moreover, this method is more practical and economical because no expensive large fatigue testing machine is needed and the specimen size is small.     

Experimental and numerical investigation of cracked chevron notched Brazilian disc specimen for fracture toughness testing of rock

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by the International Society for Rock Mechanics to quantify mode I fracture toughness (K_Ic) of rock, and it has also been applied to mode II fracture toughness (K_IIc) testing in some research on the basis of some assumptions about the crack growth process in the specimen. However, the K_Ic value measured using the CCNBD specimen is usually conservative, and the assumptions made in the mode II test are rarely assessed. In this study, both laboratory experiments and numerical modeling are performed to study the modes I and II CCNBD tests, and an acoustic emission technique is used to monitor the fracture processes of the specimens. A large fracture process zone and a length of subcritical crack growth are found to be key factors affecting the K_Ic measurement using the CCNBD specimen. For the mode II CCNBD test, the crack growth process is actually quite different from the assumptions often made for determining the fracture toughness. The experimental and numerical results call for more attention on the realistic crack growth processes in rock fracture toughness specimens.     

Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

Fracture toughness of plain concrete from three-point bend specimens

A simple method is proposed for determining the fracture toughness of plain concrete from three-point bend specimens, based on the concept of effective notch depth to account for the non-linear pre-peak load-deflection behaviour. The fracture toughness so determined is shown not to depend on the specimen size. The method improves an earlier version of the effective crack model in several ways. First, it is no longer necessary to linearize the pre-peak non-linearity, thereby eliminating the inaccurate task of establishing the limit of elastic response. Secondly, regression expressions for determining the effective notch depth should be far more accurate because they are based on an analysis of not only the authors’ test data but that of several researchers around the world. Thirdly, these expressions do not depend on the size of the test specimen. It is shown that the predictions of the effective crack model are in good agreement with two other non-linear process zone models, as far as three-point notched beam specimens are concerned.     

Study of fracture toughness evaluation of FRP

Using the fibre reinforced plastics (FRP) laminates consisting of glass chopped strand mat and unsaturated polyester resin, experiments were conducted under various conditions in order to determine the fracture toughness for crack instability. Crack growth was judged not by cracking of the resin matrix but by break of the glass fibres. The crack front was considered to be located in the section which was cracked through the 90% of the specimen thickness. Crack extension resistance (R-curves) thus obtained did not significantly vary with specimen thickness and initial crack length, but depended greatly on specimen configurations, compact tension (CT) and centre-cracked tension (CCT) specimens. The R-curve for a CT specimen was steeper than the one for a CCT specimen, which is quite contrary to the tendency for metals. It was deduced that the instability fracture toughness calculated from the maximum load on a load-deflection diagram, K _max, was scarcely affected by specimen thickness, initial crack length and specimen geometry (i.e. loading configuration), and therefore could be regarded as a material constant of the FRP used.     

木材断裂解离分形特征与分形断裂力学模型研究

目的 以椴木为研究对象,研究冲击载荷作用下椴木试件的断裂解离形貌特征和断裂力学特性,建立适用于木材原料断裂解离的分形断裂力学模型,并对其断裂解离力学行为进行描述。方法 对椴木试件进行冲击加载试验,分析试件断口的形貌特征和断裂力学特性,构建适用于木材原料断裂解离的分形断裂力学模型。结果 椴木试件横向冲击断裂断口裂纹形状和断口形貌特征比纵向冲击复杂,横、纵向冲击断裂断口均具有分形特征;椴木试件纵向冲击断裂韧性均值是横向冲击断裂韧性均值的1.112倍,椴木试件横、纵向冲击断口的分形维数均值分别为2.063 5和2.075 1,椴木试件横、纵向冲击韧性与其断口分形维数之间存在线性正相关关系,拟合优度分别为0.778 7和0.812 2;构建的木材原料断裂解离临界解离应力和断裂韧性的分形断裂力学模型也适用于脆性材料。结论 在木材原料冲击断裂解离时,木材原料初始裂纹长度越短,断裂解离断口越粗糙复杂,木材原料断裂解离所需要的能量越大;当裂纹沿着与冲击加载力方向垂直成大约1.055rad方向扩展时所需的能量最小,木材原料最易沿该方向进行断裂解离。     

Influence of silane coupling agents on interlaminar fracture in glass fibre fabric reinforced unsaturated polyester laminates

The relationship between the adhesive properties of the interphase of glass fibre/resin and the resultant composite Mode I delamination fracture toughness in glass fibre fabric laminate (GFFL) was studied. The Mode I interlaminar fracture toughness of GFFL was obtained by using a double cantilever beam (DCB) specimen. The delamination resistance of GFFLs which have two silane coupling agents and three concentration finishes is discussed on the basis of interlaminar fracture toughness. The crack propagation behaviour of DCB testing was mainly divided into stable and unstable manners. The fracture toughness and the crack propagation behaviour were dependent on the types and concentration of silane coupling agents.