Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy

The main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading.     

MODE I AND MIXED MODE I/II FATIGUE CRACKING IN Ni3Al(CrB) SINGLE CRYSTALS

Abstract— Nominal mode I and mixed mode I/II fatigue tests were carried out using the intermetallic compound Ni₃Al(CrB) in the form of single crystal specimens. The effects of crystal orientation and load mode on fatigue crack initiation and growth were studied. The fracture surfaces of the single crystals were characterized by a cleavage-like appearance and cracking occurred either on a single {111} plane or on multiple {111} planes irrespective of whether mode I or mixed mode I/II loadings were applied. It was found that the crack initiation and growth behaviour are dependent on both crystal orientation and applied loading mode. The cracking behaviour predicted by three mixed mode fracture criteria (MTS, SED and G criteria) in polycrystalline materials under mixed mode loading can be understood from the present results on single crystals.     

Estimation of the plastic zone by finite element method under mixed mode (I and II) loading

Material fracture by opening (mode I) is not lonely responsible for fracture propagation. Many industrial examples show the presence of mode II and mixed mode I + II. The present work consists in the elaboration of a code to estimate the size of the plastic zone at the crack tip under mode I, mode II and mixed mode I + II loading. The computations are made according to Von Mises and Tresca criteria. The results obtained are compared to those measured by experiments.     

Fracture of V-notched specimens under mixed mode (I + II) loading in brittle materials

The purpose of this research is threefold. First, to provide experimental results of fracture loads for V-notched beams loaded under mixed mode. Second, to check the suitability of fracture criteria based on the cohesive zone model and strain energy density when applied to those samples. And, third, to suggest a very simple fracture criterion, based on the dominance of the local mode I, for notched samples (with different V-notch angles and notch root radii) loaded under mixed (I + II) mode. This proposal unifies predictions for the experimental results obtained under mode I and mixed mode loading. To this end, 36 fracture tests on V-notched beams were performed and reported: three V-notched angles were investigated (90°, 60°, 30°, four different loadings (mixed modes I and II) were selected and three samples were tested for each configuration.     

Brittle failures from U- and V-notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite-size volumes

A large bulk of static test results carried out on notched specimens are presented in a unified way by using the mean value of the strain energy density (SED) over a given finite-size volume surrounding the highly stressed regions. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively, with R _C being the radius. R _C depends on the fracture toughness of the material, the ultimate tensile strength and the Poisson's ratio. When the notch is blunt, the control area assumes a crescent shape and R _C is its width as measured along the notch bisector.
About 900 experimental data, taken from recent literature, are involved in the local SED-based synthesis. They have been obtained from (a) U- and V-notched specimens made of different materials tested under mode I loading; (b) U- and V-notched specimens made of polymethyl-metacrylate (PMMA) and an acrylic resin, respectively, tested in mixed, I + II, mode; (c) U-notched specimens made of ceramics materials tested under mode I.
The local SED values are normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R / R _C ratio. A scatter band is obtained whose mean value does not depend on R / R _C, whereas the ratio between the upper and the lower limits are found to be about equal to 1.6. The strong variability of the non-dimensional radius R / R _C (ranging here from about zero to around 1000) makes stringent the check of the approach based on the mean value of the local SED on a material-dependent control volume.     

Fracture Assessment of U-Notched Graphite Plates Under Tension

The experimentally obtained tensile load-bearing capacity of fifteen U-notched polycrystalline graphite plates reported in literature was theoretically estimated by means of two well-known brittle fracture models, namely the mean stress (MS) and the point stress (PS) criteria. The results showed that while the mean discrepancies between the experimental and the theoretical results for both the models are very good and approximately equal, the discrepancies are significantly different for various notch tip radii. Meanwhile, the results of MS and PS criteria were compared with the results of the strain energy density (SED) criterion reported in literature. Relatively similar value of mean discrepancy was also obtained for the SED model. It was demonstrated in this research that for small values of the notch tip radius, the MS model is the most appropriate failure criterion while the PS and SED criteria are much better models for medium radii. Moreover, for large notch tip radii, the MS and PS criteria are better choices for tensile fracture assessment of U-notched graphite plates than the SED criterion.     

Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test, the end notch flexure test, the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.     

Fracture assessment of U-notches under mixed mode loading: two procedures based on the ‘equivalent local mode I’ concept

Two fracture criteria are proposed and applied to blunt-notched components made of brittle materials loaded under mixed mode; the former is based on the averaged strain energy density over a given control volume, the latter on the cohesive crack zone model. In both instances use of the equivalent local mode I hypothesis is made. Only two material properties are needed: the ultimate tensile strength and the fracture toughness. Numerical predictions of rupture loads from the two criteria are compared with experimental measurements from more than 160 static tests with notched beams. The samples are made of PMMA and tested at − 60°C to assure a bulk behaviour almost linear elastic up to rupture. Notch root radii range from 0.2 to 4.0 mm and load mixicity varies from pure mode I to a prevailing mode II. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.     

Finite element analysis of a center crack specimen warm pre-stressed under different modes of loading

Load bearing capacity of cracked specimens can be improved following pre-loading procedures like warm pre-stressing (WPS). In this paper, the effects of modes I and II pre-loading on fracture load of a central angled crack specimen are studied by finite element analysis. The specimen is reloaded either in mode I or in mode II. To predict the fracture load of cracked specimen after pre-loading, the maximum tensile stress (MTS) and maximum shear stress (MSS) criteria are used. It is shown that mode II fracture load is independent of pre-loading but the mode I fracture load is highly improved after warm pre-stressing. The mode mixity of the specimen is also changed when the pre-loading and reloading modes are not identical. An increase in the fracture load of the specimen following pre-loading may be due to change of failure mode as predicted by finite element analysis in this work.     

Analysis of a new specimen for mixed mode fracture tests on brittle materials

Numerical and experimental studies were performed on a new fracture test configuration called the diagonally loaded square plate (DLSP) specimen. The mode I and mode II stress intensity factors were computed for different crack lengths and crack orientation angles using finite element analysis. The numerical results show that the DLSP specimen is able to provide pure mode I, pure mode II and any mixed mode loading conditions in between. Fracture experiments were also conducted on Plexiglas using the DLSP specimen. It is shown that the results obtained from the fracture tests are consistent very well with mixed mode fracture theories.     

Fracture toughness of polycrystalline tungsten under mode I and mixed mode I/II loading

The fracture toughness of swaged polycrystalline tungsten was tested parallel and perpendicular to the swaging direction and under mixed mode I/mode II loading. The fracture mode is dominated by the microstructure and changed from all-transgranular cleavage in mode I to almost all-intergranular fracture in mode II. The mixed mode results can be related to two common failure criteria, the maximum tensile stress criterion (Maximum σ) and the maximum energy release rate criterion (Maximum G), but the large scatter in the data prohibits a clear distinction between the two criteria. Tests at 77 K show that the polycrystal is significantly tougher than the single crystal at this temperature. This is a consequence of the deflection of the crack into the grain boundaries and the imperfect texture (as compared to a single crystal) of the polycrystalline material.     

Investigation of softwood fracture criteria at the mesoscopic scale

In order to improve the knowledge of softwood mechanical behaviour and particularly fracture mechanisms, investigation at small scales is needed. For that purpose, new numerical tools based on the real wood morphology in the transverse plane are specifically used. A mode I fracture criterion applicable to cracks oriented in the transverse plane in softwood is then studied at the mesoscopic scale, i.e. the annual ring scale. Numerical investigation combined with digital image correlation help to obtain wood fracture parameters in the annual ring. These parameters give additional knowledge and understanding of wood fracture according to local specificities such as crack tip position in an annual ring and notch orientation in relation to natural wood orientation and loading orientation. Mesoscopic fracture criteria can help our understanding of secondary crack appearance and crack arrest phenomena. Mixed mode study and coupling between mode I and mode II of fracture will be investigated further. Mixed mode fracture criteria can then help to better understand crack bifurcation phenomenon.     

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。     

Influence of shear parameters on mixed–mode fracture of concrete

The influence of the mode II fracture parameters on the mixed mode fracture experimental tests of quasibrittle materials is studied. The study is based on experimental results and numerical analyses. For the numerical study, a procedure for mixed mode fracture of quasibrittle materials is presented. The numerical procedure is based on the cohesive crack approach, and extends it to mixed mode fracture. Four experimental sets of mixed mode fracture were modelled, one from Arrea and Ingraffea and another from a nonproportional loading by the authors, both with bending concrete beams. Two other sets of experimental fracture were modelled, based on double-edge notched testing; in these tests an important mode II is beforehand expected. The numerical results agree quite well with experimental records. The influence of the main parameters for mode II fracture on the mixed mode fracture is studied for the four experimental set of tests and compared with these results. In all them, large changes in the mode II fracture energy hardly modify the numerical results. The tangential and normal stresses along the crack path during the loading proccess are obtained, also with different values of the mode II fracture energy. For the studied experimental tests it is concluded that the crack is initiated under mixed mode but propagated under predominant mode I. This allows a development of mixed mode fracture models, mainly based on standard properties of the material measured by standard methods, avoiding the problems associated with the measurement of mode II fracture parameters, such as mode II fracture energy and cohesion.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

Evaluation of initiation criteria used in interlaminar fracture tests

The objective of this work was to evaluate the non-linearity (NL) and 5% offset or maximum load (5%-Max) criteria that are commonly used to define initiation in interlaminar fracture tests. This study is in the sequence of a previous paper where the mode I DCB and mode II ENF specimens were analysed. Finite element (FE) simulations of delamination growth were here performed for the mode II end-loaded split (ELS) and 4-point end-notched flexure (4ENF) tests. The results indicated that the formation of large process zones could affect significantly NL criteria. The maximum load point gave the most accurate toughness values, especially for the 4ENF specimen. Finally, present and previous results were compared to experimental data available in the literature.     

A novel fixture for mixed mode I/II/III fracture testing of brittle materials

A novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.     

复合型裂纹起裂角厚度效应的实验研究

完成了飞机结构铝合金LC4CS的2、4、8和14mm四种不同厚度试样在I+II复合加载条件下的复合型断裂实验,系统分析了厚度和复合载荷对裂纹起裂角的影响,揭示了常用复合型断裂准则的厚度适用范围,用三维断裂理论对结果进行了讨论。结果表明:复合型裂纹起裂角具有明显的厚度效应;最大周向应力准则能够准确预测薄试样和厚试样(厚度为2 mm 和14 mm)在各种复合加载条件下的起裂方向,但是不适用于中间厚度的试样,尤其是8 mm厚度的情况。最大三轴应力准则试图考虑裂纹尖端三维约束对裂纹起裂的影响,但是结果并不理想。最小应变能密度因子理论的预测结果与最大周向应力准则的预测结果非常接近,但同样不能预测8mm厚度试样的起裂方向。非常有必要建立一个普遍适用的三维复合型断裂准则。     

On the I–II mixed mode fracture of granite using four‐point bend specimen

Four‐point bend experiments on black granite are conducted. The fracture behaviours of granite under pure mode I, pure mode II and I–II mixed mode are investigated, and the corresponding stress intensity factors K_I , K_II and the non‐singular term T‐stress are obtained through numerical–experimental method. The results are compared with the theoretical predictions of generalized maximum tangential stress criterion and other conventional criteria. It shows that generalized maximum tangential stress criterion fits the experimental results better for considering the effect of T‐stress. Contrasting with other loading configurations, the values of T‐stress for asymmetric four‐point bend specimens are much smaller, especially for pure mode II specimens, which provide an asymmetric deformation field where the T‐stress is approaching zero.     

Effect of mixed mode I and II loading on the fracture surface of polymethyl methacrylate (PMMA)

In this paper studies conducted on Polymethyl methacrylate (PMMA) under combined bending and shear loading are described. A strong dependency of fracture surface features on the mixed mode stress state is observed. Close to pure mode I, the fracture surface is mirror-like in appearance. With increasing mode II component the fracture surface becomes misty and parabolic markings appear on the fracture surface. These observations indicate that the level of stress ahead of the crack tip increases with increasing mode II component. The mixed mode specimens are also observed to fracture at much higher stresses than the pure mode I specimen, contrary to the predictions of the fracture criteria based on linear elastic fracture mechanics (LEFM). The fracture surface features and the higher stresses at fracture in the mixed mode specimens are explained in terms of the increase in stiffness (which has been related to an increase in the effective stress intensity factor per unit opening displacement) with the introduction of a mode II component and the geometry of the 3-dimensional crack tip.