Ductile fracture initiation and propagation modeling using damage plasticity theory

Ductile fracture is often considered as the consequences of the accumulation of plastic damage. This paper is concerned with the application of a recently developed damage plasticity theory incorporates the pressure sensitivity and the Lode angle dependence into a nonlinear damage rule and the material deterioration. The ductile damaging process is calculated through the so-called “cylindrical decomposition” method. The constitutive equations are discussed and numerically implemented. An experimental and numerical investigation for three-point bending tests is reported for aluminum alloy 2024-T351. Crack initiation and propagation in compact tension specimens are also studied numerically. These simulation results show good agreement with experiments. The present model can successfully predict slant fracture as well as the formation of shear lips.     

A new fracture mechanics theory for orthotropic materials like wood

A new fracture mechanics theory is derived based on a new orthotropic-isotropic transformation of the Airy stress function, making the derivation of the Wu-“mixed mode I-II” fracture criterion possible, based on the failure criterion of a flat elliptic crack. As a result of this derivation, the right fracture energy and theoretical relation between mode I and II stress intensities and energy release rates are obtained.     

A general mixed-mode brittle fracture criterion for cracked materials

In order to predict the fracture direction and fracture loadings of cracked materials under the general mixed-mode state, this paper presents a new general mixed-mode brittle fracture criterion based on the concept of maximum potential energy release rate (MPERR). This criterion can be easily degraded to the pure-mode fracture criterion, and can also be reduced to the commonly accepted fracture criteria for the mixed-mode I/II state. In order to validate the proposed criterion, we have carried out the experiments with aluminium alloy specimens under various mixed-mode loading conditions. The experimental results agree well with the predictions of the proposed criterion.     

A non-local stress and strain energy release rate mixed mode fracture initiation and propagation criteria

A non-local stress condition for crack initiation and propagation in brittle materials is presented. This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment (damage zone) of specified length. Next, a non-local strain energy release rate criterion is proposed. This condition is based on the assumption that initiation or propagation of cracking occurs when the maximal value of the function of opening and sliding energy release rates reaches a critical value. The value of energy release rates is determined for finite elementary crack growth. Mixed mode conditions are considered, for which both the critical load value and the crack orientation are predicted from the non-local stress and energy criteria, which are applicable to both regular and singular stress concentrations. The effect of non-singular second order term (T_σ-stress) on the crack propagation is discussed.     

有限变形理论能量释放率增率形式

基于有限变形理论中的能量原理和变分原理,考虑以有裂纹的瞬时位形为参考,建立增量变形引起的裂纹扩展方程能够更真实的描述裂纹尖端的扩展机制,在含有裂纹物体的瞬时变形的基础上,推导了裂纹体的能量释放率和增率的形式,提出了裂纹扩展判据.该判据反映了单位时间内裂纹扩展单位面积可以提供的能量与单位时间内裂纹扩展单位面积所需要的能量...     

A generalized model for dynamic mixed-mode fracture via state-based peridynamics

A generalized model is developed to investigate dynamic crack propagation in isotropic solids under mixed-mode I/II conditions using state-based peridynamics. The critical stretch and the critical strain energy release rate (ERR) are related within the state-based peridynamic framework to construct a computational model capable of capturing fracture energy of the kinked cracks. A novel formulation is presented to predict crack growth trajectory and pattern by combining the traditional expression of ERR and the peridynamic states of the crack opening and sliding displacements. The proposed model is used to predict dynamic fracture behavior in polymethyl methacrylate (PMMA) and soda-lime glass using various test specimens, including cracked semi-circular bending (SCB), cracked rectangular plate, and single edge-notched tensile (SENT) specimens, and under different dynamic loading conditions. The developed model is examined against the numerical and experimental data available in the literature, and a very good agreement is observed.     

A phenomenological analysis of Mode I fracture of adhesively-bonded pultruded GFRP joints

The fracture behavior of adhesively-bonded pultruded joints was experimentally investigated under Mode I loading using double cantilever beam specimens. The pultruded adherends comprised two mat layers on each side with a roving layer in the middle. An epoxy adhesive was used to form the double cantilever beam specimen. The pre-crack was introduced in three different depths in the adherend in order to induce crack initiation and propagation between different layers and thus investigate the effect of these different crack paths on the strain energy release rate. Short-fiber and roving bridging increased the fracture resistance during crack propagation. Specific levels of critical strain energy release rates could be attributed to each of the crack paths, with their levels depending on the amount of short-fiber bridging and the presence of a roving bridge. The different levels of critical strain energy release rate could be correlated to the morphology of the fracture surface and the strain energy release rate can thus be determined visually without any measurement.     

Estimation of fracture energy from the work of fracture and fracture surface area: I. Stable crack growth

Past attempts to determine fracture energy by the work of fracture (γ _WOF) technique, in most cases, have resulted in greater estimates due to the use of the cross-sectional area rather than the actual area of the fracture surface in calculations. The actual fracture surface area A _F of soda-lime-silica glass chevron-notch flexure specimens was estimated using atomic force microscopy. An equation for A _F was developed using the data from these tests. The use of A _F in the equation for γ _WOF resulted in γ _WOF values less than values reported from traditional fracture mechanics tests and from those obtained using the cross-sectional area. The implication is that the tortuosity of the fracture surface contributes to the energy expended during fracture and should be accounted for in the calculation of the fracture energy. These calculations provide an estimate for the minimum energy required to break bonds in the fracture process.     

Determination of energy release rate and mode mix in three-dimensional layered structures using plate theory

A plate theory-based method for determining energy release rates is presented for general loadings of three dimensional layered structures. Mode decomposition is performed for cases that exhibit an inverse square root singularity and for which certain other restrictions apply. Predictions for energy release rate and mode mix for typical problems are presented and verified by comparison with results obtained by three dimensional finite element analyses.     

On a thermo-mechanical effect and criterion of crack propagation

A thermo-mechanical effect from partial conversion of fracture work into heat energy during crack propagation is considered with a simple mathematical model. It is assumed that the heat production zone in the vicinity of the crack tip is very small. Thus, the crack propagation process can be viewed as propagation of the crack in elastic material with a point thermal heat source fixed at the tip of the crack. This thermal heat source generates its own temperature and stress fields around the crack tip. As shown in this paper it also generates a negative stress intensity factor that specifies fracture mode I and has to be accounted for in the energetic fracture criterion. The model developed may help to explain many experimental observations such as the increase in the specific surface energy that accompanies an increase in the crack speed and why fracture mode I has a special role in crack propagation phenomena.     

Z-pin增强复合材料层合板断裂韧性试验研究

针对Z-pin增强复合材料层合板, 开展了断裂韧性的试验研究。研究选取了3种Z-pin直径(0.28、 0.52、 0.80mm)且每种直径下分别以3种分布形式(5×5、 8×8、 10×10)排布Z---pin的增强方式, 为了确定比较基准, 试验中同时测试了不含Z-pin的复合材料层合板试样。通过Z-pin拔出试验测试了3种直径Z-pin从基体拔出过程中的载荷位移关系。利用双悬臂梁试验和端部开口弯曲试验分别测试了不含Z-pin和含Z-pin试样的Ⅰ型断裂应变能释放率G_ⅠC、 Ⅱ型断裂应变能释放率G_ⅡC。试验结果表明:? 与不含Z-pin的结构相比, Z-pin增强试样的Ⅰ型断裂应变能释放率G_ⅠC增大了83%~1110%, Ⅱ型断裂应变能释放率G_ⅡC增大了23%~438%; 在相同Z-pin体积含量下, 与增大Z-pin直径相比, 增大Z-pin分布密度能更有效地提高复合材料层合板的断裂韧性。      

Orientation dependent fracture toughness of lamellar bone

The critical energy release rate of human bone was determined for different crack propagation directions with three-point-bending tests using controlled crack extension. The local structure was characterised by small-angle X-ray scattering, SEM and polarised light microscopy and related to the energy required for crack extension. It turns out the collagen angle is decisive for switching the fracture behaviour of bone from brittle to quasi-ductile. A significant increase in the critical energy release rate as well as a change of the appearance of the crack path from straight and smooth to deflected and zig-zag is observed.     

Modelling on crack propagation behaviours at concrete matrix‐aggregate interface

A numerical model is proposed to simulate crack propagation at concrete matrix‐aggregate interface. One single aggregate surrounded by concrete matrix is taken to demonstrate the behaviours of crack penetration into concrete matrix and crack growth along the interface. Influences of side‐edge constraint, aggregate direction, and interface fracture energy on the crack propagation behaviours are respectively investigated. The results show that, tensile constraint on the side edge, a smaller angle between tensile axis and aggregate, and higher fracture energy lead to a higher rupture strength of the interface. Once the interface crack starts to grow, it propagates to the two ends of aggregate major axis drastically and further penetrates into the matrix. Nevertheless, these factors have no appreciable influence on crack propagation path. By mapping interface crack into major axis, ordinary crack is generated. Using the above simplification, modelling of multiple crack propagation in concrete is efficiently achieved.     

Effect of stress wave propagation phenomenon on the determination of strain energy density theory parameters and dynamic J-integral

Dynamic loading for stationary cracks leads to results that are many times greater in magnitude than their static counterparts. If the dynamic loading is in the form of impact type, stress wave propagation effects become dominant. FRAC3D program comprises enriched element formulation which doesn't require excessive mesh refinement around crack tip for accuracy. Strain energy density (SED) theory parameters and dynamic J-integral are sought in this study to simulate and understand wave propagation phenomenon in detail. Structures under the effect of wave propagations yield more reliable J-integral values by taking the average of the results from multiple domain sizes. Governed by stress waves, space-time variations of minimum energy density locations strongly influence fracture characterization for straight and curved crack fronts. Details given in numerical examples section of this paper make a great contribution to understanding of the response for cracked structures subjected to sudden loading.     

A creep model with damage based on internal variable theory and its fundamental properties

The creep damage is discussed within Rice irreversible internal state variable (ISV) thermodynamic theory. An ISV small-strain unified creep model with damage is derived by giving the complementary energy density function and kinetic equations of ISVs. The proposed model can describe viscoelasticity and, preferably, three phases of creep deformation. Creep strain results from internal structural adjustment, and different creep stages accompany different thermodynamic properties in terms of flow potential function and energy dissipation rate. During the viscoelastic process, the thermodynamic state of the material system tends to equilibrate spontaneously. The thermodynamic state of the material system without damage tends to equilibrate or achieve steady state after loading. Kinetic equations of ISVs can be derived by one single flow potential function, and the energy dissipation rate decreases monotonically over time. In the entire creep damage process, multiple potentials are needed to characterise evolution of ISVs, rotational fluxes are presented in affinity space, and the thermodynamic state of material system tends to depart from the steady or equilibrium state. The energy dissipation rate can be a measure of the distance between the current thermodynamic state and the equilibrium state. The time derivative of the rate can characterise the development trend of the material, and the integral value in the domain may be regarded as indices to evaluate the long-term stability of the structure.     

Investigation of fatigue and fracture properties of asphalt mixtures modified with carbon nanotubes

Load‐induced cracking is one of the primary forms of distress in asphalt pavements at intermediate temperatures. Binder modification is a good alternative to promote the cracking resistance of asphalt mixtures. In the current research study, the effects of carbon nanotubes as a binder modifier on the fatigue and fracture performance of asphalt mixtures are investigated. The carbon nanotubes are added at five different percentages ranging from 0.2% to 1.5% to the base binder to study their effects on the fracture resistance and fatigue life of the asphalt mixtures. Using the cracked semi‐circular bend specimen, the critical value of J‐integral (Jc) was obtained for the investigated modified asphalt mixtures. Also, the fatigue behaviour of asphalt mixtures was studied using flexural beam fatigue test specimen. By employing the ratio of dissipated energy change approach, the plateau value of tested mixtures was determined as a measure of fatigue performance. Results showed that the carbon nanotubes can enhance both fracture resistance and fatigue performance of tested asphalt mixtures especially at higher percentages of the carbon nanotube.     

On the dynamic crack propagation in an interphase with spatially varying elastic properties under inplane loading

This article provides a comprehensive theoretical investigation on a finite crack with constant length (Yoffe type crack) propagating in an interfacial layer with spatially varying elastic properties under inplane loading. The analytical formulations are developed using Fourier transforms and solving the resulting singular integral equations in terms of the opening and sliding displacements of the crack. The dynamic stress intensity factors and energy release rate are analyzed to study the dynamic fracture property of this inherent mixed mode crack problem. Numerical examples are provided to show the effects of the material properties, the thickness of the interfacial layer, the crack position and speed upon the dynamic fracture behaviour, and the singularity transition between the current crack and the corresponding interfacial crack for thin interphase.     

New Strengthening Techniques with FRP Laminates and Interfacial Fracture Theories

The use of FRP composites in the form of sheet or plate bonded to the large-scale RC structures is becoming an increasing attractive solution to the strengthening of existing structures. Compared with traditional steel plate strengthening, FRP possesses excellent behavior such as lightness in weight, high strength-to-weight and stiffness-to-weight ratio, high corrosion and fatigue resistance, electronic neutrality, and great efficiency in construction. A important failure mode for FRP-strengthened structures is debondings.Therefore, the LEFM and NLFM are utilized to treat this problem. Closed form expressions for energy release rate, load-carrying capacity, load-displacement relation and interfacial crack propagation are obtained, in which a local shear stress-slip law with softening is adopted.     

A new look at energy release rate in fracture mechanics

The energy balance for fracture in elastic/perfectly plastic solids is examined using the finite element method. An extension-release procedure that gives numerically converged solutions is employed in the numerical simulation of crack extensions in elastic/plastic solids. Increments of work and energy during crack extension are calculated for various loading conditions. Several conclusions are obtained. First, the elastic separation work of creating new crack surfaces is shown to be negligible, indicating that the Griffith-type energy release does not exist. Second, as the yield stress increases, the plastic dissipation work rate associated with crack extension converges to the energy release rate in the limiting elastic solid. The latter result can be adopted to interpret the classical energy release rate in elastic solids as plastic dissipation work rate taken in the limit as the yield stress approaches infinity during crack extension. Lastly, it is shown that the energy release rate obtained according to Irwin's plastic zone adjustment approach is equal to the plastic dissipation work rate for the original crack, provided the plastic zone size is less than 10% of the original crack size.     

Predicting fracture of solder joints with different constraint factors

Double cantilever beam (DCB) specimens of 2.5‐mm‐long SAC305 solder joints were prepared with thickness of copper adherends varying from 8 to 21 mm each. The specimens were tested under mode I loading conditions (ie, pure opening mode with no shear component of loading) with a strain rate of 0.03 second^?1. The measured fracture load was used to calculate the critical strain energy release rate for crack initiation, J_ci, in each case. Fracture behaviour showed a significant dependence on the adherend thickness; the J_ci and plastic deformation of the solder at crack initiation decreased significantly with increase in adherend thickness. This behaviour was attributed to changes in stress distribution along the solder layer when the adherend thickness was varied. The capability of J_ci as a property was then assessed to predict the fracture load of solder joints in specimens with different constraint levels caused by variations in adherend thicknesses. In light of the results obtained, a cohesive zone model (CZM) was developed to predict the fracture load of solder joints as a function of adherend thickness. Finally, a CZM with a single set of parameters was established to predict the fracture loads for all the cases. It was concluded that CZM was a better methodology to account for changes in degree of joint constraint imposed by bonding adherends.