Christopher Harvey | Loughborough University (original) (raw)

Papers by Christopher Harvey

Theoretical and Applied Fracture Mechanics, 2017

A hypothesis is made that delamination can be driven by pockets of energy concentration (PECs) in... more 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 systems.

Nature Communications, Dec 5, 2017

Interface adhesion toughness between multilayer graphene films and substrates is a major concern ... more Interface adhesion toughness between multilayer graphene films and substrates is a major concern for their integration into functional devices. Results from the circular blister test, however, display seemingly-anomalous behaviour as adhesion toughness depends on number of graphene layers. Here we show that interlayer shearing and sliding near the blister crack tip, caused by the transition from membrane stretching to combined bending, stretching and through-thickness shearing, decreases fracture mode mixity GII/GI, leading to lower adhesion toughness. For silicon oxide substrate and pressure loading, mode mixity decreases from 232% for monolayer films to 130% for multilayer films, causing the adhesion toughness Gc to decrease from 0.424 J m-2 to 0.365 J m-2. The mode I and II adhesion toughnesses are found to be GIc = 0.230 J m-2 and GIIc = 0.666 J m-2 respectively. With point loading, mode mixity decreases from 741% for monolayer films to 262% for multilayer films, while the adhesion toughness Gc decreases from 0.543 J m-2 to 0.438 J m-2.

Composite Structures, Dec 15, 2016

Previous work by the authors (Harvey et al., 2015) on brittle interfacial cracking between two di... more Previous work by the authors (Harvey et al., 2015) on brittle interfacial cracking between two dissimilar elastic layers is extended to accommodate Poisson’s ratio mismatch in addition to the existing capability for elastic modulus mismatch. Under crack tip bending moments and axial forces, it is now possible to use a completely analytical 2D elasticity-based theory to calculate the complex stress intensity factor (SIF) and the crack extension size-dependent energy release rates (ERRs). To achieve this, it is noted that for a given geometry and loading condition, the total ERR and bimaterial mismatch coefficient are the two main factors affecting the partitions of ERR. Based on this, equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson’s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be ‘transformed’ into cases for which the analytical solution does exist. The approach is verified against results from 2D finite element method simulations in which excellent agreement is observed for cases of plane stress and plane strain with a variety of loading conditions.

Engineering Fracture Mechanics, Jun 1, 2017

Tolpygo and Clarke (2000) presented an excellent experimental study on the room temperature circu... more 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.

Composite Structures, Aug 1, 2016

An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic lam... more 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.

Composite Structures, Dec 1, 2015

Analytical theories are developed for post-local buckling-driven delamination in bilayer composit... more Analytical theories are developed for post-local buckling-driven delamination in bilayer composite beams. The total energy release rate (ERR) is obtained more accurately by including an axial strain energy contribution from the intact part of the beam and by developing a more accurate expression for the post-buckling mode shape than that in the work by Chai et al. (1981) and Hutchinson and Suo (1992). The total ERR is partitioned by using partition theories based on the Euler beam, Timoshenko beam and 2D-elasticity theories. Independent experimental tests by Kutlu and Chang (1995) show that, in general, the analytical partitions based on the Euler beam theory predicts the propagation behaviour very well and much better than the partitions based on the Timoshenko beam and 2D-elasticity theories.

Composite Structures, Dec 15, 2015

Fracture on bimaterial interfaces is an important consideration in the design and application of ... more 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).

Composite Structures, Dec 15, 2015

A thorough program of 2D finite element method (FEM) simulations is carried out parametrically on... more 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).

Three different approaches to partitioning mixed-mode delaminations are assessed for their abilit... more Three different approaches to partitioning mixed-mode delaminations are assessed for their ability to predict the interfacial fracture toughness of generally laminated composite beams. This is by using published data from some thorough and comprehensive experimental tests carried out by independent researchers (Davidson et al., 2000 and 2006). Wang and Harvey’s (2012) Euler beam partition theory is found to give very accurate prediction of interfacial fracture toughness for arbitrary layups, thickness ratios and loading conditions. Davidson et al.’s (2000) non-singular-field partition theory has excellent agreement with Wang and Harvey’s Euler beam partition theory for unidirectional layups. Although Davidson et al.’s partition theory predicts the interfacial fracture toughness of multidirectional layups reasonably well, overall Wang and Harvey’s Euler beam partition theory is found to give better predictions. In general, the singular-field approach based on 2D elasticity and the finite element method gives poor predictions of fracture toughness.

A powerful method for partitioning mixed-mode fractures on rigid interfaces in laminated unidirec... more A powerful method for partitioning mixed-mode fractures on rigid interfaces in laminated unidirectional double cantilever beams (DCBs) is developed by taking 2D elasticity into consideration in a novel way. Pure modes based on 2D elasticity are obtained by introducing correction factors into the beam-theory-based mechanical conditions. These 2D-elasticity-based pure modes are then used to derive a 2D-elasticity-based partition theory for mixed-mode fractures. Excellent agreement is observed between the present partition theory and Suo and Hutchinson’s partition theory [1]. Furthermore, the method that is developed in this work has a stronger capability for solving more complex mixed-mode partition problems, for example, in the bimaterial case.
[1] Suo Z, Hutchinson JW. Interface crack between two elastic layers. International Journal of Fracture Mechanics 1990;43:1–18.

The authors’ existing mixed-mode partition theories for rigid interfaces are extended to non-rigi... more The authors’ existing mixed-mode partition theories for rigid interfaces are extended to non-rigid cohesive interfaces for layered isotropic double cantilever beams. Within the context of Euler beam theory, it is shown that the two sets of orthogonal pure modes coincide at the first set of pure modes due to the absence of any crack tip stress singularity for a non-rigid interface. The total energy release rate in a mixed mode is then partitioned using this first set of pure modes without considering any ‘stealthy interaction’. Within the context of Timoshenko beam theory, it is shown that the mode II component of energy release rate is the same as that in Euler beam theory while the mode I component is different due to the through-thickness shear effect. Within the context of 2D elasticity, a mixed-mode partition theory is developed using the two sets of orthogonal pure modes from Euler beam theory with rigid interfaces and a powerful orthogonal pure mode methodology. Numerical simulations are conducted to verify the theories.

Completely analytical theories are presented for the mixed-mode partitioning of one-dimensional d... more Completely analytical theories are presented for the mixed-mode partitioning of one-dimensional delamination in laminated composite beams. The work builds on previous research by the authors on one-dimensional fractures in layered isotropic beams. The partition theories are developed within the contexts of both Euler and Timoshenko beam theories. Two sets of orthogonal pairs of pure modes are found and used to partition mixed modes. Approximate ‘averaged partition rules’ are also established for 2D elasticity. The beam partition theories and averaged rules are extensively validated against numerical simulations using the finite element method (FEM). The contact behavior of double cantilever beams (DCBs) is also investigated. Two types of contact exist: crack tip running contact, which results in a region of pure mode II; and point contact at the DCB tip, which can result in either in mixed modes or pure mode II.

A robust numerical method is developed to study delamination in composite beam structures under l... more A robust numerical method is developed to study delamination in composite beam structures under lateral and axial loads. A tensor symmetrisation technique is used to formulate the beam element based on the Euler beam theory with full geometrical non-linearity to achieve high computational efficiency. Ply interfaces are modelled with high-stiffness springs. It is found that the beam element suffers from membrane locking for non-symmetric laminates. A method is found to overcome it. The model is used to simulate double cantilever composite beam structure tests and end notched flexure tests. Excellent agreement is observed with analytical and existing numerical and experimental data. The model is also used to study the buckling, post-buckling and delamination propagation in moderately thick composite beams. Satisfactory agreement is demonstrated between the present predictions and existing numerical and experimental data. It is noted that the through-thickness shear effect is significant for moderately thick composite laminates.

The propagation of mixed-mode interlaminar fractures is investigated using existing experimental ... more The propagation of mixed-mode interlaminar fractures is investigated using existing experimental results from the literature and various partition theories. These are (i) a partition theory by Williams (1988) based on Euler beam theory; (ii) a partition theory by Suo (1990) and Hutchinson and Suo (1992) based on 2D elasticity; and (iii) the Wang-Harvey partition theories of the authors based on the Euler and Timoshenko beam theories. The Wang-Harvey Euler beam partition theory seems to offer the best and most simple explanation for all the experimental observations. No recourse to fracture surface roughness or new failure criteria is required. It is in excellent agreement with the linear failure locus and is significantly closer than other partition theories. It is also demonstrated that the global partition of energy release rate when using the Wang-Harvey Timoshenko beam or averaged partition theories or 2D elasticity exactly corresponds with the partition from the Wang-Harvey Euler beam partition theory. It is therefore concluded that the excellent performance of the Wang-Harvey Euler beam partition theory is either due to the failure of materials generally being based on global partitions or that for the specimens tested, the through-thickness shear effect is negligibly small. Further experimental investigations are definitely required.

The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. I... more The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. It has caused considerable confusion due to its in-depth subtleness and complex entanglement with different theories and numerical simulations. The present paper presents completely analytical theories based on Euler and Timoshenko beam theories using a brand new approach which reveals the hidden mechanics of the problem. Orthogonal pairs of pure modes are found and used to partition mixed modes. The developed theories are extensively validated against numerical simulations using finite element methods. Moreover, the fracture mode partition space is thoroughly investigated and crack tip running contact is found which results in a region of pure mode II. The theories are finally applied to general one-dimensional fracture in beams and axisymmetric plates.

A completely analytical theory is developed for the mixed mode partition of one-dimensional fract... more 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.

AIP Conference Proceedings, Dec 1, 2012

A numerical method is developed to predict delamination propagation in composite laminated beam s... more A numerical method is developed to predict delamination propagation in composite laminated beam structures under lateral and axial loads. Full geometrical nonlinearity is included in the development of beam elements and the interfaces are modeled with imaginary interface springs. The one step crack closure technique, a contact algorithm and tensor symmetrization are employed in the formulation. It is found that asymmetric composite beam elements suffer from membrane locking and this is completely solved in the work. Also, the mode partitioning results are different to those from the existing mode partition theory. A new theory is developed which shows the flaw in the existing theory and demonstrates the validity of the imaginary interface spring model. In general, excellent agreement with existing numerical and experimental results is observed.

Taking a double cantilever beam (DCB) as a representative of one dimensional fracture, a unique p... more 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 rate.

Theoretical and Applied Fracture Mechanics, 2017

A hypothesis is made that delamination can be driven by pockets of energy concentration (PECs) in... more 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 systems.

Nature Communications, Dec 5, 2017

Interface adhesion toughness between multilayer graphene films and substrates is a major concern ... more Interface adhesion toughness between multilayer graphene films and substrates is a major concern for their integration into functional devices. Results from the circular blister test, however, display seemingly-anomalous behaviour as adhesion toughness depends on number of graphene layers. Here we show that interlayer shearing and sliding near the blister crack tip, caused by the transition from membrane stretching to combined bending, stretching and through-thickness shearing, decreases fracture mode mixity GII/GI, leading to lower adhesion toughness. For silicon oxide substrate and pressure loading, mode mixity decreases from 232% for monolayer films to 130% for multilayer films, causing the adhesion toughness Gc to decrease from 0.424 J m-2 to 0.365 J m-2. The mode I and II adhesion toughnesses are found to be GIc = 0.230 J m-2 and GIIc = 0.666 J m-2 respectively. With point loading, mode mixity decreases from 741% for monolayer films to 262% for multilayer films, while the adhesion toughness Gc decreases from 0.543 J m-2 to 0.438 J m-2.

Composite Structures, Dec 15, 2016

Previous work by the authors (Harvey et al., 2015) on brittle interfacial cracking between two di... more Previous work by the authors (Harvey et al., 2015) on brittle interfacial cracking between two dissimilar elastic layers is extended to accommodate Poisson’s ratio mismatch in addition to the existing capability for elastic modulus mismatch. Under crack tip bending moments and axial forces, it is now possible to use a completely analytical 2D elasticity-based theory to calculate the complex stress intensity factor (SIF) and the crack extension size-dependent energy release rates (ERRs). To achieve this, it is noted that for a given geometry and loading condition, the total ERR and bimaterial mismatch coefficient are the two main factors affecting the partitions of ERR. Based on this, equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson’s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be ‘transformed’ into cases for which the analytical solution does exist. The approach is verified against results from 2D finite element method simulations in which excellent agreement is observed for cases of plane stress and plane strain with a variety of loading conditions.

Engineering Fracture Mechanics, Jun 1, 2017

Tolpygo and Clarke (2000) presented an excellent experimental study on the room temperature circu... more 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.

Composite Structures, Aug 1, 2016

An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic lam... more 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.

Composite Structures, Dec 1, 2015

Analytical theories are developed for post-local buckling-driven delamination in bilayer composit... more Analytical theories are developed for post-local buckling-driven delamination in bilayer composite beams. The total energy release rate (ERR) is obtained more accurately by including an axial strain energy contribution from the intact part of the beam and by developing a more accurate expression for the post-buckling mode shape than that in the work by Chai et al. (1981) and Hutchinson and Suo (1992). The total ERR is partitioned by using partition theories based on the Euler beam, Timoshenko beam and 2D-elasticity theories. Independent experimental tests by Kutlu and Chang (1995) show that, in general, the analytical partitions based on the Euler beam theory predicts the propagation behaviour very well and much better than the partitions based on the Timoshenko beam and 2D-elasticity theories.

Composite Structures, Dec 15, 2015

Fracture on bimaterial interfaces is an important consideration in the design and application of ... more 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).

Composite Structures, Dec 15, 2015

A thorough program of 2D finite element method (FEM) simulations is carried out parametrically on... more 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).

Three different approaches to partitioning mixed-mode delaminations are assessed for their abilit... more Three different approaches to partitioning mixed-mode delaminations are assessed for their ability to predict the interfacial fracture toughness of generally laminated composite beams. This is by using published data from some thorough and comprehensive experimental tests carried out by independent researchers (Davidson et al., 2000 and 2006). Wang and Harvey’s (2012) Euler beam partition theory is found to give very accurate prediction of interfacial fracture toughness for arbitrary layups, thickness ratios and loading conditions. Davidson et al.’s (2000) non-singular-field partition theory has excellent agreement with Wang and Harvey’s Euler beam partition theory for unidirectional layups. Although Davidson et al.’s partition theory predicts the interfacial fracture toughness of multidirectional layups reasonably well, overall Wang and Harvey’s Euler beam partition theory is found to give better predictions. In general, the singular-field approach based on 2D elasticity and the finite element method gives poor predictions of fracture toughness.

A powerful method for partitioning mixed-mode fractures on rigid interfaces in laminated unidirec... more A powerful method for partitioning mixed-mode fractures on rigid interfaces in laminated unidirectional double cantilever beams (DCBs) is developed by taking 2D elasticity into consideration in a novel way. Pure modes based on 2D elasticity are obtained by introducing correction factors into the beam-theory-based mechanical conditions. These 2D-elasticity-based pure modes are then used to derive a 2D-elasticity-based partition theory for mixed-mode fractures. Excellent agreement is observed between the present partition theory and Suo and Hutchinson’s partition theory [1]. Furthermore, the method that is developed in this work has a stronger capability for solving more complex mixed-mode partition problems, for example, in the bimaterial case.
[1] Suo Z, Hutchinson JW. Interface crack between two elastic layers. International Journal of Fracture Mechanics 1990;43:1–18.

The authors’ existing mixed-mode partition theories for rigid interfaces are extended to non-rigi... more The authors’ existing mixed-mode partition theories for rigid interfaces are extended to non-rigid cohesive interfaces for layered isotropic double cantilever beams. Within the context of Euler beam theory, it is shown that the two sets of orthogonal pure modes coincide at the first set of pure modes due to the absence of any crack tip stress singularity for a non-rigid interface. The total energy release rate in a mixed mode is then partitioned using this first set of pure modes without considering any ‘stealthy interaction’. Within the context of Timoshenko beam theory, it is shown that the mode II component of energy release rate is the same as that in Euler beam theory while the mode I component is different due to the through-thickness shear effect. Within the context of 2D elasticity, a mixed-mode partition theory is developed using the two sets of orthogonal pure modes from Euler beam theory with rigid interfaces and a powerful orthogonal pure mode methodology. Numerical simulations are conducted to verify the theories.

Completely analytical theories are presented for the mixed-mode partitioning of one-dimensional d... more Completely analytical theories are presented for the mixed-mode partitioning of one-dimensional delamination in laminated composite beams. The work builds on previous research by the authors on one-dimensional fractures in layered isotropic beams. The partition theories are developed within the contexts of both Euler and Timoshenko beam theories. Two sets of orthogonal pairs of pure modes are found and used to partition mixed modes. Approximate ‘averaged partition rules’ are also established for 2D elasticity. The beam partition theories and averaged rules are extensively validated against numerical simulations using the finite element method (FEM). The contact behavior of double cantilever beams (DCBs) is also investigated. Two types of contact exist: crack tip running contact, which results in a region of pure mode II; and point contact at the DCB tip, which can result in either in mixed modes or pure mode II.

A robust numerical method is developed to study delamination in composite beam structures under l... more A robust numerical method is developed to study delamination in composite beam structures under lateral and axial loads. A tensor symmetrisation technique is used to formulate the beam element based on the Euler beam theory with full geometrical non-linearity to achieve high computational efficiency. Ply interfaces are modelled with high-stiffness springs. It is found that the beam element suffers from membrane locking for non-symmetric laminates. A method is found to overcome it. The model is used to simulate double cantilever composite beam structure tests and end notched flexure tests. Excellent agreement is observed with analytical and existing numerical and experimental data. The model is also used to study the buckling, post-buckling and delamination propagation in moderately thick composite beams. Satisfactory agreement is demonstrated between the present predictions and existing numerical and experimental data. It is noted that the through-thickness shear effect is significant for moderately thick composite laminates.

The propagation of mixed-mode interlaminar fractures is investigated using existing experimental ... more The propagation of mixed-mode interlaminar fractures is investigated using existing experimental results from the literature and various partition theories. These are (i) a partition theory by Williams (1988) based on Euler beam theory; (ii) a partition theory by Suo (1990) and Hutchinson and Suo (1992) based on 2D elasticity; and (iii) the Wang-Harvey partition theories of the authors based on the Euler and Timoshenko beam theories. The Wang-Harvey Euler beam partition theory seems to offer the best and most simple explanation for all the experimental observations. No recourse to fracture surface roughness or new failure criteria is required. It is in excellent agreement with the linear failure locus and is significantly closer than other partition theories. It is also demonstrated that the global partition of energy release rate when using the Wang-Harvey Timoshenko beam or averaged partition theories or 2D elasticity exactly corresponds with the partition from the Wang-Harvey Euler beam partition theory. It is therefore concluded that the excellent performance of the Wang-Harvey Euler beam partition theory is either due to the failure of materials generally being based on global partitions or that for the specimens tested, the through-thickness shear effect is negligibly small. Further experimental investigations are definitely required.

The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. I... more The crack in a double cantilever beam is the most fundamental one-dimensional fracture problem. It has caused considerable confusion due to its in-depth subtleness and complex entanglement with different theories and numerical simulations. The present paper presents completely analytical theories based on Euler and Timoshenko beam theories using a brand new approach which reveals the hidden mechanics of the problem. Orthogonal pairs of pure modes are found and used to partition mixed modes. The developed theories are extensively validated against numerical simulations using finite element methods. Moreover, the fracture mode partition space is thoroughly investigated and crack tip running contact is found which results in a region of pure mode II. The theories are finally applied to general one-dimensional fracture in beams and axisymmetric plates.

A completely analytical theory is developed for the mixed mode partition of one-dimensional fract... more 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.

AIP Conference Proceedings, Dec 1, 2012

A numerical method is developed to predict delamination propagation in composite laminated beam s... more A numerical method is developed to predict delamination propagation in composite laminated beam structures under lateral and axial loads. Full geometrical nonlinearity is included in the development of beam elements and the interfaces are modeled with imaginary interface springs. The one step crack closure technique, a contact algorithm and tensor symmetrization are employed in the formulation. It is found that asymmetric composite beam elements suffer from membrane locking and this is completely solved in the work. Also, the mode partitioning results are different to those from the existing mode partition theory. A new theory is developed which shows the flaw in the existing theory and demonstrates the validity of the imaginary interface spring model. In general, excellent agreement with existing numerical and experimental results is observed.

Taking a double cantilever beam (DCB) as a representative of one dimensional fracture, a unique p... more 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 rate.