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

Structure mechanical modeling of thin-walled closed- section composite beams, part 2: multi-cell cross section

The methodology used in part 1 [1] of the work for single-cell thin-walled closed-section composite beams is extended to multi-cell thin-walled closed-section composite beams. The effect of material anisotropies is fully considered on the mid-surface shear strain of all the cross sectional members including skin walls and internal members. Numerical comparisons with ABAQUS finite element simulations are performed for three-cell box and elliptical beams with a variety of laminate layups under various loading conditions and excellent agreements are observed. Significant deficiency of some existing models are shown

Limit cycles in Lienard equations

An analytical estimation of the existence and characteristics of limit cycles in a given planar polynomial vector field represents a significant progress towards the complete answer to the second part of Hilbert’s 16th problem. In a very recent work [1], the second author of this present paper has developed a theory to fulfil this purpose. One major conclusion of the theory is that the number of limit cycles nested around a critical point in a general planar polynomial vector field is bounded by the Hilbert number where n is the order of the vector field. It is well known that linear vector fields have no limit cycles and this, of course agrees with the conclusion. Shi [2] shows that there are maximum three limit cycles nested around a critical point in quadratic vector fields. Again, it is in an agreement with the conclusion. For cubic vector fields results from previous studies [3,4,5] are also in an agreement with the conclusion whilst the result from the work [6] is in a disagreement although there exists some doubt about the result. In this present work, a detailed study is given to the limit cycles in a fifteenth order Liénard equation by using both the theory [1] and numerical simulations to check the validity of the theory. The method of analysis is briefly given in Section 2. An application example and conclusions are presented in Section 3 and 4, respectively

On fracture mode partition theories

Wang and Harvey (2009 and 2010), and Wang and Guan (2010) have developed fracture mode partition theories for one-dimensional fractures in beams and plates based on both classical and shear deformable beam and plate theories. This paper presents comparisons between different theories and numerical simulations to validate the developed theories

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

A theory of one-dimensional fracture

A completely analytical theory is developed for the mixed mode partition of one-dimensional fracture in laminated composite beams and plates. Two sets of orthogonal pure modes are determined first. It is found that they are distinct from each other in Euler beam or plate theory and coincide at the Wang-Harvey set in Timoshenko beam or plate theory. After the Wang- Harvey set is proved to form a unique complete orthogonal pure mode basis within the contexts of both Euler and Timoshenko beam or plate theories, it is used to partition a mixed mode. Stealthy interactions are found between the Wang-Harvey pure mode I modes and mode II modes in Euler beam or plate theory, which alter the partitions of a mixed mode. The finite element method is developed to validate the analytical theories

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)

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