On mixed-mode fracture in layered materials.

This paper reports the authors’ recent work on partition theories of energy release rate (ERR) for 1D fracture in fiber-reinforced laminated composite beams and plates. A novel and powerful methodology is created to partition the total ERR based on beam and 2D elasticity theories

Mixed mode partition in one dimensional fractures

Taking a double cantilever beam (DCB) as a representative of one dimensional fracture, a unique pair of pure fracture modes I and II are successfully found in the absence of axial forces, which are orthogonal to each other with respect to the coefficient matrix of the energy release rate. Although the pair are pure modes there still exist interactions between them. The interactions result in energy flow between the two modes and are successfully determined. With the presence of axial forces, there are two independent pure modes I and two independent pure modes II, which are orthogonal to each other as well. They are found and used to partition the total energy release rat

Brittle interfacial cracking between two dissimilar elastic layers: part 2-numerical verification

A thorough program of 2D finite element method (FEM) simulations is carried out parametrically on a bimaterial double cantilever beam (DCB) model in MSC/NASTRAN. The Young's modulus ratio, the Poisson's ratio, the thickness ratio, and the DCB tip loads are varied over their entire practically useful domains for different values of the crack extension size. Extensive comparisons are made between the results of the analytical theory that was developed in Part 1 by Harvey et al. (2015) and FEM results. This paper reports the outcome of these comparisons. The present analytical theory and the supporting mathematical techniques are thoroughly verified. Overall, excellent agreement is observed between the present analytical theory and the FEM results for the crack extension size-dependent energy release rate (ERR) components and the stress intensity factors (SIFs)

The mechanics of interface fracture in layered composite materials: (5) thin film spallation driven by pockets of energy concentration – microscopic interface fracture

A hypothesis is made that delamination can be driven by pockets of energy concentration (PECs) in the form of pockets of tensile stress and shear stress on and around the interface between a thin film and a thick substrate, where PECs can be caused by thermal, electrochemical or other processes. Based on this hypothesis, three analytical mechanical models are developed to predict several aspects of thinfilm spallation failure including nucleation, stable and unstable growth, size of spallation and final kinking off. The predictions from the developed models are compared against experimental results and excellent agreement is observed

Room temperature spallation of α-alumina films grown by oxidation

Tolpygo and Clarke (2000) presented an excellent experimental study on the room temperature circular spallation of α-alumina films grown by oxidation on Fe-Cr-Al alloy. Their observations are remarkable and thought-provoking and are worthy of mechanical interpretation. The present work hypothesizes that pockets of energy concentration (PECs) exist due to dynamic and non-uniform plastic relaxation or creep in the film and Fe-Cr-Al alloy substrate during cooling. PECs may be the driving energy for room temperature spallation failure. Based on this hypothesis, an analytical mechanical model is developed in this work to predict the spallation behavior, including the separation nucleation, stable and unstable growth, and final spallation and kinking off. The predictions from the developed model are compared against experimental results and excellent agreement is observed. The work reveals a completely new failure mechanism of thin layer materials

The mechanics of interface fracture:(2) cohesive interfaces

The authors’ existing mixed-mode partition theories for rigid interfaces are extended to nonrigid cohesive interfaces for layered isotropic double cantilever beams. The two sets of orthogonal pure modes for rigid interfaces coincide with each other for cohesive interfaces. Excellent agreement is observed between the analytical theory and finite element simulations

Brittle interfacial cracking between two dissimilar elastic layers: part 1-analytical development

Fracture on bimaterial interfaces is an important consideration in the design and application of composite materials and structures. It has, however, proved an extremely challenging problem for many decades to obtain an analytical solution for the complex stress intensity factors (SIFs) and the crack extension size-dependent energy release rates (ERRs), based on 2D elasticity. This work reports such an analytical solution for brittle interfacial cracking between two dissimilar elastic layers. The solution is achieved by developing two types of pure fracture modes and two powerful mathematical techniques. The two types of pure fracture modes are a SIF type and a load type. The two mathematical techniques are a shifting technique and an orthogonal pure mode technique. Overall, excellent agreement is observed between the analytical solutions and numerical simulations by using the finite element method (FEM). This paper reports the analytical development of the work. The numerical verification using the FEM is reported in Part 2 by Harvey, Wood and Wang (2015)

Partition of mixed-mode fractures in 2D elastic orthotropic laminated beams under general loading

An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic laminated double cantilever beams (DCBs) under through-thickness shear forces, in addition to bending moments and axial forces, is developed by extending recent work by the authors (Harvey et al., 2014). First, two pure through-thickness-shear-force modes (one pure mode I and one pure mode II) are discovered by extending the authors’ mixed-mode partition theory for Timoshenko beams. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II energy release rate (ERR) correction factor. Both correction factors closely follow an elegant normal distribution around a symmetric DCB geometry. The principle of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a general loading condition, including bending moments, axial forces, and through-thickness shear forces. Excellent agreement is observed between the present analytical partition theory and numerical results from finite element method (FEM) simulations

Spallation of thin films driven by pockets of energy concentration

A hypothesis is made that delamination can be driven by pockets of energy concentration (PECs) in the form of pockets of tensile stress and shear stress on and around the interface between a thin film and a thick substrate, where PECs can be caused by thermal, chemical or other processes. Based on this hypothesis, three analytical mechanical models are developed to predict several aspects of the spallation failure of elastic brittle thin films including nucleation, stable and unstable growth, size of spallation and final kinking off. Both straight-edged and circular-edged spallations are considered. The three mechanical models are established using partition theories for mixed-mode fracture based on classical plate theory, first-order shear-deformable plate theory and full 2D elasticity. Experimental results show that all three of the models predict the initiation of unstable growth and the size of spallation very well; however, only the 2D elasticity-based model predicts final kinking off well. The energy for the nucleation and stable growth of a separation bubble comes solely from the PEC energy on and around the interface, which is ‘consumed’ by the bubble as it nucleates and grows. Unstable growth, however, is driven both by PEC energy and by buckling of the separation bubble. Final kinking off is controlled by the fracture toughness of the interface and the film and the maximum energy stored in the separation bubble. This work will be particularly useful for the study of spallation failure in thermal barrier coating material system

Mixed-mode delamination in layered isotropic and laminated composite beam structures

Completely analytical theories are presented for calculating the total energy release rate (ERR) in a mixed-mode delamination in layered isotropic and laminated composite straight beam structures and for partitioning it into opening mode I and shearing mode II components. The theories are developed within the contexts of both the Euler and Timoshenko beam theories. The theories are extensively verified against numerical simulations using the finite element method. The developed theories provide a valuable means for the design of such beam structures against delamination