Failure prediction in toughened epoxy resins

In order to improve the damage tolerance of composites and the performance of adhesives, one of the methods being considered is toughened or modified epoxy resins. The modifiers which are commonly used are CTBN rubber and inorganic fillers. A major toughening mechanism causing the increased toughness is the shear deformation process occurring near the crack tip. The effect of such a deformation process is to blunt the crack tip and increase the size of the plastic zone. Several models are available to predict the toughness on the basis of plastic zone size, crack tip opening displacement or crack tip radius, but these are only applicable to Mode I crack extension. Also, most of these approaches use only one stress component which is normal to the crack plane to predict the fracture toughness. The present paper reviews the existing models and suggests a criterion based on the phenomenological approach to failure in order to study the yielding and fracture toughness behavior of both unmodified and modified epoxies. The proposed yield and fracture criteria give predictions in good agreement with experimental results.     

黏聚裂纹阻抗的弯曲梁承载力

在混凝土类软化材料断裂研究中,裂纹端部损伤区被简化为具有黏聚应力分布的非线性裂纹,该黏 聚力对裂纹扩展有阻抗作用。裂纹体的应力强度因子是断裂力学标志载荷作用与几何构型因素的量化表达指标; 黏聚力形成的阻抗强度因子数值,与黏聚裂纹长度和材料极值拉伸应力存在数量关系。通过双K断裂判据,以 带切口的三点弯曲梁为断裂力学模型,分析了裂纹黏聚阻力对断裂过程的影响规律,计算该弯曲梁结构断裂试 样的最大承担载荷;其结果比较符合实验数据。     

Efficient prediction of deterministic size effects using the scaled boundary finite element method

This paper develops an efficient numerical approach to predict deterministic size effects in structures made of quasi-brittle materials using the scaled boundary finite element method (SBFEM). Depending on the structure’s size, two different SBFEM-based crack propagation modelling methodologies are used for fracture analyses. When the length of the fracture process zone (FPZ) in a structure is of the order of its characteristic dimension, nonlinear fracture analyses are carried out using the finite element-SBFEM coupled method. In large-sized structures, a linear elastic fracture mechanics (LEFM)-based SBFEM is used to reduce computing time due to small crack propagation length required to represent the FPZ in an equivalent nonlinear analysis. Remeshing is used in both methods to model crack propagation with crack paths unknown a priori. The resulting peak loads are used to establish the size effect laws. Three concrete structures were modelled to validate the approach. The predicted size effect is in good agreement with experimental data. The developed approach was found more efficient than the finite element method, at least in modelling LEFM problems and is thus an attractive tool for predicting size effect.     

The effect of constraint on creep fracture assessments

This paper describes a preliminary examination of the effect of in-plane constraint on creep crack growth under widespread creep conditions using the Q stress. Plane strain is assumed. Damage models for fracture of the process zone based on both ductility exhaustion and stress rupture are shown to predict a variation of the crack growth rate with Q. Lower levels of constraint lead to lower crack growth rates for a given C*. The results are used to outline a high temperature failure assessment diagram approach to constraint-dependent creep crack growth. This revised version was published online in July 2006 with corrections to the Cover Date.     

Size effect on fracture resistance and fracture energy of concrete

A recent asymptotic approach dealing with the size effect on the fracture properties of a large plate is further developed to consider the influence of both the front and back free surfaces of small sized specimens. The new extension is applied to experimental results found in the literature, and good agreements have been found between the predictions and the fracture resistance and energy measured using geometrically similar specimens and specimens with identical size but different initial crack or notch lengths. The physics behind the size effect are discussed based on the modified asymptotic approach. It is found that both the specimen geometry and crack length contribute to the size effect on fracture properties besides its physical size. In particular, the ratio of a fracture process zone, size over its distance to a free surface plays a very important role.     

Crack growth criteria incorporating non-singular stresses: Size effect in apparent fracture toughness

Simple criteria accounting for the non-singular stresses at the crack tip are considered. They are based on the comparison of the local stress concentration with the material microstrength. The local stress concentration is estimated either as the magnitude of the conventional elastic stress ahead of the process zone, or by its averaging over the process zone length. When a criterion of this type is used to find the critical load and then the conventional fracture toughness, the latter will be dependent of the crack length. This size effect in fracture toughness manifests itself as an increase (if the non-singular part of the near-tip stress field is positive) or decrease (if the non-singular part is negative) in the apparent fracture toughness as the crack length increases. The obtained dependence is compared with available experimental data. It is also shown that when the load can be resolved into a superposition of elementary loads, the size effect can asymptotically (for long cracks) be presented as a weighted sum of the elementary size effects (i.e. the size effects associated with the elementary loads) with the weights equal to the relative contributions of the elementary loads into the total stress intensity factor. This revised version was published online in August 2006 with corrections to the Cover Date.     

EFFECTS OF CRACK LENGTH, NOTCH ROOT RADIUS AND GRAIN SIZE ON FRACTURE TOUGHNESS OF FINE CERAMICS

Generally, fracture toughness and fracture stress of ceramics depend on crack length, notch root radius and grain size. These three parameters are most important when assessing the integrity of structural ceramic members and developing high-performance ceramics. A new failure criterion called the process zone size failure criterion, has been proposed based on the existence of a crack-tip process zone. Using this criterion, it is shown that theoretical values are in good agreement with many test results quoted from many papers. It is concluded that this failure criterion is useful when evaluating crack length and notch root radius problems. The effect of grain size on both the fracture toughness and on the toughening mechanism is also considered.     

The effect of microstructure and stress state on the fracture behaviour of wood

Based on a general fracture mechanics approach, this paper attempts to correlate macroscopic fracture properties with micromechanical behaviour in wooD. In the first part, the influence of orientation, cell size and other structural features of wood on toughness, fatigue resistance and fracture morphology is described. Subsequently, experimental observations of crack tunnelling effects are reported which, coupled with direct crack tip strain measurements and a verification of the influence of specimen thickness on fracture properties, confirm the existence of stress state variations across a crack front in wood, and the corresponding effects on fracture behaviour. Irreversible crack-tip deformation modes are identified, involving intercellular debonding, cell twisting and buckling, and the role of stress triaxiality is discussed. A strain criteria for the fracture of pre-notched bulk wood specimens is developed, based on an observed linear relationship between notch root radius and crack opening displacement for fracture initiation.     

The effect of constraint on creep fracture assessments

This paper describes a preliminary examination of the effect of in-plane constraint on creep crack growth under widespread creep conditions using the Q stress. Plane strain is assumed. Damage models for fracture of the process zone based on both ductility exhaustion and stress rupture are shown to predict a variation of the crack growth rate with Q. Lower levels of constraint lead to lower crack growth rates for a given C*. The results are used to outline a high temperature failure assessment diagram approach to constraint-dependent creep crack growth. This revised version was published online in August 2006 with corrections to the Cover Date.     

Connecting the essential work of fracture, stress intensity factor, Hill’s criterion in mixed mode I/II loading

Ductile sheet structures are frequently subjected to mixed mode loading, resulting that the structure is under the influence of a mixed mode stress field. Instances of interest are when stable crack growth occurs and when the crack-tip is propagating in this complex mixed-mode condition, prior to final fracture. Purposely designed apparatus was built to test thin-sheets of steel (Grade: DX51D) under mixed-mode I/II. These tests, under plane stress conditions, also investigated the effect of thickness on the specific essential work of fracture or the fracture toughness of the material under quasi-static cracking conditions. The fracture toughness is evaluated under incremental mixed-mode loading conditions. The direction of the propagating crack path and fracture type were observed and discussed as the loading mixity was varied. Whilst the specific essential work of fracture or fracture toughness was obtained using the energy approach, the theoretical analysis of the fracture type and direction of crack path were based on the crack tip stresses and fracture criterions of maximum hoop stress and maximum shear stress along with the utilisation of Hill’s theory. For mixed-mode I/II loading, the variation in the fracture toughness contributions ratios are evaluated and used predicatively using the established energy criterion approach to the crack tip stress intensity approach. The comparison between the theoretical directions of the crack path, failure mode propagation are in good agreement with those obtained from experimental testing indicating the definite link between both approaches.     

Simulations of dynamic crack propagation in brittle materials using nodal cohesive forces and continuum damage mechanics in the distinct element code LDEC

Experimental data indicates that the limiting crack speed in brittle materials is less than the Rayleigh wave speed. One reason for this is that dynamic instabilities produce surface roughness and microcracks that branch from the main crack. These processes increase dissipation near the crack tip over a range of crack speeds. When the scale of observation (or mesh resolution) becomes much larger than the typical sizes of these features, effective-medium theories are required to predict the coarse-grained fracture dynamics. Two approaches to modeling these phenomena are described and used in numerical simulations. The first approach is based on cohesive elements that utilize a rate-dependent weakening law for the nodal cohesive forces. The second approach uses a continuum damage model which has a weakening effect that lowers the effective Rayleigh wave speed in the material surrounding the crack tip. Simulations in this paper show that while both models are capable of increasing the energy dissipated during fracture when the mesh size is larger than the process zone size, only the continuum damage model is able to limit the crack speed over a range of applied loads. Numerical simulations of straight-running cracks demonstrate good agreement between the theoretical predictions of the combined models and experimental data on dynamic crack propagation in brittle materials. Simulations that model crack branching are also presented.     

Mesh scalability in direct finite element simulation of brittle fracture

A new approach of dealing with mesh dependence in finite element modelling of fracture processes is introduced. In particular, in brittle fracture modelling, the stress concentration is mesh dependent as the results do not stabilise when refining the mesh. This paper presents an approach based on the explicit incorporation of mesh dependence into the computations. The dependence of the relevant stress is quantified on the finite elements at the crack tip upon the element size; when the dependence approaches a power law with the required accuracy, the mesh is called scalable. If the mesh is scalable and the exponent and pre-factor are known, then the results of the computations can be scaled to the size relevant to the scale of the physical microstructure of the material; the latter while not being modelled directly ultimately controls the fracture propagation. To illustrate this new approach, four 2D examples of a single straight crack loaded under tensile and shear tractions applied either to the external boundary or to the crack faces are considered. It is shown that combining the stresses at the crack tip computed using a set of similar meshes of different densities with the crack tip asymptotic allows accurate recovery of the stress intensity factors.     

Numerical estimation of the fatigue crack front shape for a specimen with finite thickness

An iterative process for the estimation of a fatigue crack front based on linear elastic fracture mechanics using values of the stress singularity exponent is presented. Based on the assumption of a constant stress singularity exponent along the crack front, a numerical approach leading to crack shape determination is suggested and applied. The crack front was approximated by a spline curve. In each node defining the crack front the stress singularity exponent was estimated and a complete crack front shape was found. The difference between thin and thick specimens is then described and discussed. The approach presented leads to better estimation of the crack front shape for structures with different thicknesses and a more accurate determination of fatigue crack fracture parameters. The results presented can be helpful for a better understanding of fatigue failure and more reliable prediction of residual lifetime.     

On the effect of quarter-point element size on fracture criteria

The effect of the quarter-point element size on the solution parameters of fracture criteria is investigated in view of its effect on the computed stress intensity factors. An analytical relationship between the error in calculating crack propagation increment and stress intensity for single mode problems is obtained while, for mixed mode problems, the investigation is based on numerical experimentation. The singular element size is found to have a substantial effect on both crack propagation angle and increment for the geometries considered.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

Interface fracture in adhesively bonded shell structures

Two methods for the prediction of crack propagation through the interface of adhesively bonded shells are discussed. One is based on a fracture mechanics approach; the other is based on a cohesive zone approach. Attention is focussed on predicting the shape of the crack front and the critical stress required to propagate the crack under quasi-static conditions. The fracture mechanical model is theoretically sound and it is accurate and numerically stable. The cohesive zone model has some advantages over the fracture mechanics based model. It is easier to generalise the cohesive zone model to take into account effects such as plastic deformation in the adhering shells, and to take into account effects of large local curvatures of the interface crack front. The comparison shows a convergence of the results based on the cohesive zone model towards the results based on a fracture mechanics approach in the limit where the size of the cohesive zone becomes smaller than other relevant geometrical lengths for the problem. However, convergence issues and numerical stability must be addressed.     

Automatic crack growth prediction in rails with BEM

Durability and damage tolerance calculations are typically based on experimental data or analytical studies of simplified cases. In this paper, a new numerical approach is described which can be used with the full model loading to compute the stress intensity factors and also to automatically predict how cracks will propagate.The benefits of the full numerical computation of the stress field are numerous, accurate prediction of crack growth, improved stress intensity data and more accurate prediction of life, thus providing an accurate method for the forensic analysis of failures.The crack growth process can be modelled with a variety of crack growth models relating the rate of crack growth to the computed stress intensity factors. The crack growth itself can include the effects of multiple load cases including the effect of residual stress fields.The crack growth process itself is fully automated by automatically re-meshing the crack surface and the nearby surfaces of the structure. The crack growth process is aided by the use of a fracture wizard that enables the necessary components for the analysis to be selected and the analysis to be controlled.Applications will be presented describing the potential applications of the method to the growth of cracks in rail components.     

An analysis of fracture under biaxial loading using the non-singular T-stress

Finite element analysis using a two-dimensional modified-boundary-layer approach was used to model the effects of biaxial loading on crack tip stress fields. Loadings were applied corresponding to an elastic KI field, non-singular T-stress and a biaxial stress. For through-thickness cracks the T-stress inherent in the specimen geometry is augmented by the external biaxial stress. For surface-notched specimens the biaxial stress acts out of the crack plane. This effect was modelled with generalized plane strain elements. Results were analysed using the Anderson-Dodds approach for cleavage and the Beremin model in the ductile regime. Biaxial loading is predicted to have a large effect on the toughness of a through-thickness crack but little effect on a surface crack. Experimental results from a previous series of large-scale biaxial fracture tests are generally consistent with these predictions.     

Fatigue life prediction for stainless steel welded plate CCT geometry based on Lawrence''s local-stress approach

In the present study, the effect of welding process and procedure on fatigue crack initiation from notches and fatigue crack propagation in AISI 304L stainless steel welds was experimentally investigated. Full penetration, double-vee butt welds have been fabricated and CCT type specimens were used. Lawrence's local-stress approach (a two-stage model) is used to predict the fatigue life. The notch-root stress method was applied to calculate the fatigue crack initiation life, while the fatigue crack propagation life was estimated using fracture mechanics concepts. The fatigue notch factor is calculated using Lawrence's approach. Constant amplitude fatigue tests with stress ratio, R=0 were carried out using 100 kN servo-hydraulic DARTEC universal testing machine with a frequency of 30 Hz. The predicted lives were compared with the experimental values. A good agreement has been reached. It is found that the weld procedure has a stronger effect on lives to initiation than on propagation lives.     

紧凑四点剪切砼Ⅱ型断裂实验研究与数值分析

有关Iosipescu四点剪切实验的争论很多,国内外的研究者提出了各种各样的结果。本文对紧凑四点剪切加载下砼Ⅱ型断裂破坏机理进行了大量的实验研究和数值分析。通过对实验中试件裂纹的扩展过程及开裂角cq等的分析,结合有限元法对裂尖应力场进行了研究。分析了加载点与裂纹面的距离对Ⅱ型断裂性能的影响。可以看出,虽然随着加载点与裂纹面距离的缩短,CKⅡ在逐渐增大,但纯剪加载下裂纹扩展并不是沿剪应力所在方向,即破坏并不是剪切破坏。