Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.     

Effect of a graded layer on the plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

Prior work by the authors has proposed a dissipated energy theory of fatigue crack growth in ductile solids under mode I loading based on the total plastic dissipation per cycle ahead of the crack. The approach has since been extended to a general bimaterial interface geometry under mixed-mode I/II loading, with application to fatigue debonding of layered materials. An inherent assumption of this prior work is that a perfect crack exists along the interface between the two materials. The current work extends the approach to incorporate a grading of material properties between the two layers, as may occur in a variety of welding, soldering or layered manufacturing applications. Attention is restricted to elastic perfectly-plastic layers with identical elastic properties and a mismatch in yield strength across a linearly graded interface, with the crack on the boundary of the weaker material. A dimensionless plastic dissipation is extracted from 2-D plane strain finite element models over the full range of yield strength mismatches, graded layer thicknesses and mixed-mode loading conditions. Results reveal that for all modes of loading, the effect of a graded layer is to increase the total plastic dissipation per cycle, which is bounded by the extremes in plastic mismatch for a perfect crack interface. While the graded layer has a measurable effect, the plastic dissipation for all strength mismatches is dominated by the mode of loading.     

On the size of plastic zone ahead of crack tip

A method for the crack tip analysis of a tensile loaded crack (mode I) due to yielding of the material is developed. The stress/strain distribution within the plastic zone, as well as size of the plastic zone are presented. The development is based on the energy interpretation of the strain hardening exponent, and an analogy between mode III and mode I for the case of small scale yielding. Predictions of the proposed method are compared with the experimental results, and a fairly good agreement is observed. A number of proposed methods to estimate the plastic zone size for ductile materials are also discussed.     

On the dynamics of localization and fragmentation—III. Effect of cladding with a polymer

In this series of papers, we investigate the mechanics and physics of necking and fragmentation in ductile materials. The behavior of ductile metals at strain rates of about 4,000–15,000 per second is considered. The expanding ring experiment is used as the vehicle for examining the material behavior in this range of strain rates. In Part I, the details of the experiment and the experimental observations on Al 6061-O were reported. Statistics of necking and fragmentation were evaluated and the process was modeled through the idea of the Mott release waves both from necking and fragmentation. Finally, it was shown that the strain in the ring never exceeded the necking strain in regions that strained uniformly. In Part II, we addressed the issues of strain hardening, ductility, geometry and size. Specifically, we examined different materials—Al 1100-H14, and Cu 101—and concluded that geometric constraint influences the strain at onset of localization significantly. The time taken for the localization to propagate across the cross-section and begin to unload its neighborhood was shown to control the amount of strain that can be experienced by the material; this also influences the statistics of localization and fragmentation. In the present paper, Part III, we examine the influence of compliant polymeric claddings on the localization and fragmentation response of metallic materials. Thin aluminum rings were coated with a layer of polyurea, with the thickness being an important parameter in the study. The onset of necking localization is shown not to be influenced by the coating; however, the propagation of unloading or release waves is shown to be significantly impeded by the cladding and therefore, further straining and fragmentation of the rings is affected. This result is of great importance in determining the impact resistance of elastomer-clad metallic structures. In future contributions as part of this sequel, we will explore the effect the development of localization and fragmentation in tubes and sheets where the geometric constraint can be varied over an even larger range.     

Studies on the fracture mechanics parameters of weldment with mechanical heterogeneity

The fully plastic solutions of welded centre-cracked strip for plane stress problem were carefully investigated with the fully plastic finite element method. It was introduced for assessing the fracture mechanics parameters of weldment with mechanical heterogeneity that there existed an equivalent yielding stress and equivalent strain hardening exponent in the vicinity of crack tip keeping the assessment of fracture mechanics parameters of weldment in the same way as the homogeneous material. The equivalent yielding stress and equivalent strain hardening exponent of various matched weldment were computed and the effect of weld metal width were calculated and discussed on equivalent yielding stress and equivalent strain hardening exponent near crack tip. The engineering approach was given for estimating the fracture mechanics parameters of weldment with mechanical heterogeneity in elastic-plastic range.     

Flexural behaviour of UHTCC‐layered concrete composite beam subjected to static and fatigue loads

As an engineered material, ultra‐high toughness cementitious composite (UHTCC) exhibits the characteristics of pseudo strain hardening and multiple cracking under uniaxial tension. It can be applied as the reinforcing and protective material of concrete structures. In this paper, static and fatigue flexural tests were carried out on UHTCC‐layered concrete composite beams, for which UHTCC layer was used on the tension side. Under both static and fatigue loads, plane section assumption was suitable for such composite beams, and a good bond strength was achieved between the two layers. For static specimens, the UHTCC layer enhanced the ductility of the concrete layer. While under cyclic loads, because of the reinforcing effect of UHTCC, more than one crack were formed in the concrete layer, which led to a ductile deformation. Furthermore, the fatigue damage process of the composite beam was analysed.     

Fracture toughness of layered structures: Embrittlement due to confinement of plasticity

The fracture toughness of a layered composite material is analyzed employing a combined two dimensional dislocation dynamics (DD)-cohesive zone (CZ) model. The fracture mechanism of an elastic-plastic (ductile) material sandwiched within purely elastic layers approaches ideally brittle behaviour with decreasing layer thickness. We investigate the influence of different constitutive parameters concerning dislocation plasticity as well as the effect of cohesive strength of the ductile material on the scaling of fracture toughness with layer thickness. For a constant layer thickness, the results of the numerical model are consistent with the expectation that fracture toughness decreases with increasing yield strength, but increases with the cohesive strength of the material. The scaling behaviour of the fracture toughness with layer thickness depends on these material parameters, but also on the dislocation microstructure in the vicinity of the crack tip. Strain localization due to easy dislocation generation right at the crack tip improves toughness in thin layers and leads to a jump-like increase of fracture toughness with layer thickness. However, the fracture toughness for films that are thick enough to exhibit bulk behaviour proves to be higher when the distribution of dislocations is more homogeneous, because in this case the crack grows in a stable fashion over some distance.     

Non—Local Analysis of Forming Limits of Ductile Material Considering Void Growth

The current study performed a finite element analysis of the strain localization behavior of a voided ductile material using a non-local plasticity formulation in which the yield strength depends on both an equivalent plastic strain measurement (hardening parameter) and Laplacian equivalent. The introduction of gradient terms to the yield function was found to play an important role in simulating the strain localization behavior of the voided ductile material. The effect of the mesh size and characteristic length on the strain localization were also investigated. An FEM simulation based on the proposed non-local plasticity revealed that the load-strain curves of the voided ductile material subjected to plane strain tension converged to one curve, regardless of the mesh size. In addition, the results using non-local plasticity also exhibited that the dependence of the deformation behavior of the material on the mesh size was much less sensitive than that with classical local plasticity and could be successfully eliminated through the introduction of a large value for the characteristic length.     

A combined dislocation—cohesive zone model for fracture in a confined ductile layer

The collective dislocation behavior near a crack tip in a ductile layer sandwiched between two brittle solids is analyzed via two-dimensional dislocation dynamics (DD) simulations that incorporate a cohesive zone (CZ) model. The cohesive crack tip is treated as part of a much larger finite crack confined in the ductile layer. The underlying boundary value problem is formulated with a set of boundary integral equations and numerically evaluated with a collocation method. The fracture energy of the layered composite material is shown to be strongly correlated with the layer thickness and is directly influenced by the cohesive strength of the ductile layer (Hsia KJ et al. (1994) J Mech Phys Solids 6 877–896).     

Fracture behavior of nano-layered coatings under tension

The fracture of brittle/ductile multilayers composed of equal thicknesses of Si and Ag layers evaporated on a thick substrate is studied with the aid of a four-point bending apparatus. The system variables include individual layer thickness (2.5 to 30 nm), total film thickness (0.5 to 3.5 μm) and substrate material (polycarbonate, aluminum alloy and hard steel). The fracture is characterized by transverse cracks that proliferate with load. The crack initiation strain ε_i is virtually independent of total film thickness and substrate material while increasing with decreasing layer thickness h, to a good approximation as ε_i ~ 1/h^1/2. At higher strains, film debonding and buckling are evident.The fracture conditions are determined with the aid of a 2D finite element analysis incorporating the inelastic response of the interlayer. A fracture scenario consisting of tunnel cracking in the brittle layers followed by cracking in the interlayers is shown to be capable of predicting the observed increase in crack initiation strain with decreasing layer thickness. To realize this benefit the interlayer must be compliant and tough to force tunnel cracking in the brittle layers. The explicit relation for the crack initiation strain obtained from the analysis can be used to assess fracture toughness and improve damage tolerance in nanoscale layered structures.     

A modified cohesive zone model for a high‐speed expanding crack

The present work studies a self‐similar high‐speed expanding crack of mode‐I in a ductile material with a modified cohesive zone model. Compared with existing Dugdale models for moving crack, the new features of the present model are that the normal stress parallel to crack faces is included in the yielding condition in the cohesive zone and traction force in the cohesive zone can be non‐uniform. For a ductile material defined by von Mises criterion without hardening, the present model confirms that the normal stress parallel to crack face increases with increasing crack speed and can be even larger than the normal traction in the cohesive zone, which justifies the necessity of including the normal stress parallel to the crack faces in the yielding condition at high crack speed. In addition, strain hardening effect is examined based on a non‐uniform traction distribution in the cohesive zone.     

The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates

The uniaxial compressive responses of silicone rubber (B452 and Sil8800) and pig skin have been measured over a wide range of strain rates (0.004–4000 s⁻¹). The uniaxial tensile response of the silicone rubbers was also measured at low strain rates. The high strain rate compression tests were performed using a split-Hopkinson pressure bar made from AZM magnesium alloy. High gain semi-conductor strain gauges were used to detect the low levels of stress (1–10 MPa), and a pulse shaper increased the rise time of dynamic loading on the specimen. The experiments reveal that pig skin strain hardens more rapidly than silicone rubbers and has a greater strain rate sensitivity: pig skin stiffens and strengthens with increasing strain rate over the full range explored, whereas silicone rubber stiffens and strengthens at strain rates in excess of 40 s⁻¹. A one term Ogden strain energy density function adequately describes the measured constitutive response of each solid, and a strategy is outlined for determining the associated material constants (strain hardening exponent and a shear modulus). The strain rate sensitivities of the pig skin and two silicone rubbers are each quantified by an increase in the shear modulus with increasing strain rate, with no attendant change in the strain hardening exponent. It is shown that the Mooney-Rivlin model is unable to describe the strong strain hardening capacity of these rubber-like solids.     

Liner and nonlinear elastic analysis of cracked plate: Application of a penalty function and superposition method

Cracked plates of power hardening material under plane strain and incompressibility conditions are investigated in this work by using a penalty function and superposition method. The present numerical method is found to be quite efficient for the relevant problems if the hardening exponent of material is not so large.     

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J₂ incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.     

A finite element analysis of plane strain dynamic crack growth in materials displaying the Bauschinger effect

In this paper dynamic crack growth in an elastic-plastic material is analyzed under mode I plane strain small-scale yielding conditions using a finite element procedure. The main objective of this paper is to investigate the influence of anisotropic strain hardening on the material resistance to rapid crack growth. To this end, materials that obey an incremental plasticity theory with linear isotropic or kinematic hardening are considered. A detailed study of the near-tip stress and deformation fields is conducted for various crack speeds. The results demonstrate that kinematic hardening does not oppose the role of inertia in decreasing the plastic strains and stresses near the crack tip with increase in crack speed to the same extent as isotropic strain hardening. A ductile crack growth criterion based on the attainment of a critical crack opening displacement at a small micro-structural distance behind the tip is used to obtain the dependence of the theoretical dynamic fracture toughness with crack speed. It is found that for any given level of strain hardening, the dynamic fracture toughness displays a much more steep increase with crack speed over the quasi-static toughness for the kinematic hardening material as compared to the isotropic hardening case.     

弯管壁厚减薄与材料特性关系的试验研究

在管材弯曲变形的系列研究中,为了分析导致弯管外侧壁厚减薄的各种影响因素,及材料机械性能对管材弯曲成形性及其各种成形缺陷产生的影响,进行了管材状态下的材料拉伸实验,其结果与同种材料的标准拉伸实验得到的性能参数相比,有一定差异.针对1C18Ni9Ti管材性能参数与部分弯曲实验结果进行的比较和定性分析表明,无论弯管外侧材料处于单向或双向不等拉伸状态,管壁厚减薄量都随材料的硬化指数和延伸率增大而增加,且随材料的屈强比增大而减小.     

Scaling of energy dissipation in crushing and fragmentation: a fractal and statistical analysis based on particle size distribution

An extensive experimental investigation on concrete specimens under crushing and fragmentation over a large scale range (1:10) – exploring even very small specimen dimensions (1 cm) – was carried out to evaluate the influence of fragment size distribution on energy density dissipation and related size effect. To obtain a statistically significant fragment production as well as the total energy dissipated in a given specimen, the experimental procedure was unusually carried out up to a strain of approximately –95%, practically corresponding to the initial fragment compaction between the loading platens. The experimental fragment analysis suggests a fractal law for the distribution in particle size; this simply means that fragments derived from a given specimen appear geometrically self-similar at each observation scale. In addition, clear size effects on dissipated energy density are experimentally observed. Fractal concepts permit to quantify the correlation between fragment size distribution and size effect on dissipated energy density, the latter being governed by the total surface area of produced fragments. The experimental results agree with the proposed multi-scale interpretation satisfactorily.