Griffith Energy Balance Research Articles

A frost heave pressure model for fractured rocks subjected to repeated freeze-thaw deterioration

Rock engineering in the Tibetan Plateau is usually suffered severe freeze-thaw (F-T) deterioration, triggering numerous geotechnical engineering disasters. As the essential triggering factor of F-T damage, the frost heave pressure (FHP) in rocks should be quantitatively described and predicted. In this study, a novel theoretical model is established and validated to estimate the critical entire evolution process of FHP in fractured rocks subjected to repeated F-T deterioration, in which the influence of fracture geometric configuration, rock mechanical properties and F-T conditions are comprehensively considered. Besides, given the obvious five-stage manner of FHP evolution, the combination effect of different dominant mechanisms in different stages is theoretically addressed. During freezing, after a silence stage induced by temperature above freezing point of water, volumetric expansion and frost-heave cracking separately controls the generation and reduction stages of FHP, and the solutions are obtained based on elastic mechanics and Griffith energy balance theory, respectively. During thawing, ice segregation dominates the second-arising stage of FHP that is quantitatively described via segregation potential and water migration velocity, and then the FHP enters the dissipation stage owing to complete melting of fracture ice. In addition, a decay coefficient is introduced to estimate the influence of F-T cycle number on FHP, and a piecewise FHP model is finally constructed for fractured rocks subjected to repeated F-T deterioration. To validate our new model, a total of 12 F-T cycle tests with real-time FHP monitoring are conducted on granite and sandstone specimens considering three typical influencing factors, i.e., fracture width, rock types and freezing temperatures. A rational consistency is identified between the theoretical and testing results in terms of the FHP evolution curves and the peak FHPs in rock fracture, demonstrating the generalizability and robustness of our proposed model.

Modulating adhesion strength in multi-ferroic composite materials: Insights from adhesive contact with arbitrary profile indenters

Adhesion control is a critical aspect of various applications, from industrial adhesion devices to the locomotion of insects on ceilings and walls. Multi-ferroic materials, which encompass mechanical, electrical, and magnetic properties, offer approaches for reversible adhesion control. This study presents a comprehensive theoretical framework for adhesive contact in multi-ferroic composite materials when subjected to axisymmetric rigid indenters with arbitrary profiles. We analytically derive the physical fields for various contact models, including Hertz contact, Johnson–Kendall–Roberts (JKR), and Maugis–Dugdale (MD) adhesive models. The obtained energy release rates indicate that the electric and magnetic potentials can modulate adhesion strength. The Griffith energy balance relation is employed to derive the indentation forces and penetration depths, which can be extended to a range of common indenters. Notably, the classical approximations fail when using small spherical indenters, but the study provides valid alternatives. The influence of amplitude and wavelength on contact behavior is explored, with greater effects observed for larger or smaller values. For cosine-shaped indenters, equivalence to flat-ended cylindrical punches is established under specific conditions. The study also reveals that the power indices for power-law-shaped indenters change the influence of electric and magnetic potentials on pull-off forces. These findings provide a theoretical fundament associated with the biomimetic and artificial adhesive systems and the modern testing techniques.

A unified treatment of axisymmetric adhesive contact for piezoelectric materials

Nanoindentation technique has been widely applied to characterize the electromechanical properties of piezoelectric materials, where the adhesion effect induced by different surface forces becomes very prominent. The indenter tip should have more general profile rather than just three common simple shapes (flat, cone and sphere) in practical testing. In this study, the classical Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models are extended to investigate the adhesion behaviors of a piezoelectric half-space indented by the power-law shaped punches with different electric properties, whose shape index is denoted as n. The JKR-n and M-D-n adhesion models for both the electrically conducting and electrically insulating punches are set up by means of Griffith energy balance. The Derjaguin-Muller-Toporov-n (DMT-n) adhesion solutions are derived from the corresponding M-D-n adhesion models as the limiting cases. The generalized Tabor parameter and interfacial adhesion strength applicable to piezoelectric materials are defined for the first time, with the former being used to describe the transition behavior from JKR-n model to DMT-n model. The impacts of the electric loading and the shape index on adhesion behaviors are discussed in detail. It is found that the pull-off force increases with the electric potential, which reveals the adhesion strengthening effect caused by electric loading. The shape index has a prominent influence on the pull-off force, interfacial adhesion strength, contact radius at pull-off moment, indentation depth and contact radius at self-equilibrium state, and the transition behavior from JKR-n model to DMT-n model. The results derived from this work not only are helpful to understand the contact behaviors of piezoelectric materials at micro/nano scale, but also provide a theoretical basis for nanoindentation technique in evaluating material properties of piezoelectric mediums.

Atomistic insight into the defect-induced tunable plasticity and electronic properties of tetragonal zirconia

Tetragonal zirconia (t-ZrO2) with exceptional properties is crucial in catalytic applications. Defects effectively enhance its electronic properties and plasticity, making t-ZrO2 a valuable material for high-efficiency industrial catalysts, and flexible electronic devices. In this study, we utilize first-principles calculations to compare the impact of vacancy defects and nitrogen doping on the structural and electronic properties of wide bandgap semiconductor t-ZrO2. Additionally, we analyze the tuned plasticity of t-ZrO2 by varying N-dopant and vacancy concentrations using molecular dynamics simulations and cyclic-nanoindentation tests. The estimation of energy release associated with plastic deformation is conducted using the Griffith energy balance model. Our study reveals significantly distinct electronic properties and plastic deformation maps in oxygen-deficient and N-doped t-ZrO2 compared to the perfect counterpart, where the defect nature dictates the band gap energy and plastic zone size. t-ZrO2−x exhibits a greater bandgap narrowing than t-ZrO2−xNx, resulting from increased atomic displacement, decreased free energy for plastic deformation, and enhanced plastic dissipated energy. Furthermore, we demonstrate that electronic properties and the plasticity of t-ZrO2−xNx, including bandgap energy and energy release rate during cyclic-nanoindentation, are unable to compete with those of the small-bandgap counterpart t-ZrO2−x. Herein, t-ZrO2−x, x = 0.2 exhibits the highest plasticity and the smallest bandgap of 1.28 eV, contrasting with the 5.6 eV bandgap of perfect t-ZrO2. Thereby, t-ZrO2−x displays pronounced band gap tightening and enriched flexibility, providing it a favorable semiconductor for photoelectrochemical energy conversion (PEC) applications.

A modified single edge V-notched beam method for evaluating surface fracture toughness of thermal barrier coatings

The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed (APS) thermal barrier coatings (TBCs). As APS TBCs are typical multilayer porous ceramic materials, the direct applications of the traditional single edge notched beam (SENB) method that ignores those typical structural characters may cause errors. To measure the surface fracture toughness more accurately, the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered. In this paper, a modified single edge V-notched beam (MSEVNB) method with typical structural characters is developed. According to the finite element analysis (FEA), the geometry factor of the multilayer structure is recalculated. Owing to the narrower V-notches, a more accurate critical fracture stress is obtained. Based on the Griffith energy balance, the reduction of the crack surface caused by micro-defects is corrected. The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.

The Effect of Adhesion on Indentation Behavior of Various Smart Materials

The nanoindentation technique plays a significant role in characterizing the mechanical properties of materials at nanoscale, where the adhesion effect becomes very prominent due to the high surface-to-volume ratio. For this paper, the classical adhesion theories were generalized to study the contact behaviors of various piezoelectric materials indented by conical punches with different electric properties. With the use of the Hankel integral transform, dual integral equations, and superposing principle, the closed-form solutions of the physical fields for the Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models were obtained, respectively. The contribution of the electrical energy to the energy release rate under the conducting punch was taken into consideration. The relationships between the contact radius, the indentation load, and the indentation depth were set up using the total energy method for the JKR model and the Griffith energy balance for the M-D model, respectively. Numerical results indicate that increasing the half cone angle of the conical punch enhances the adhesion effect, which can significantly affect the accuracy of the results of characterization in nanoindentation tests. It was found that the effect of electric potential on adhesion behaviors is sensitive to different material properties, which are not revealed in the existing studies of axisymmetric adhesive contact of piezoelectric materials and multiferroic composite materials. The load-displacement curves under conical punches with different half cone angles have very different slopes. These results indicate that the half cone angle has a prominent effect on the characterization of mechanical properties of piezoelectric solids in nanoindentation tests.

Adhesive behavior between dissimilar materials subjected to thermo-elastic loadings with normal-tangential coupling effect

The temperature difference always exists between contacting objects in various thermal bonding technologies, where the adhesion strength is found to be very sensitive to the temperature. In this paper, the anisothermal adhesive contact between an elastic cylinder subjected to the external force with an inclined angle and an elastic substrate is investigated based on the non-slipping JKR model, where the coupling effect between the normal and tangential tractions within the contact region is taken into consideration. The stated problem is reduced to a system of coupled singular integral equations, which can be solved with the analytical function theory. The full analytical solutions of the oscillatory stress fields are obtained for the first time by taking the series expansion of the integrand induced by the thermoelastic effect, which is of substantial significance. The relationship between the contact size and the external loadings is established by virtue of the Griffith energy balance criterion. The difference between the oscillatory and non-oscillatory solutions of stress fields is discussed in detail. Numerical results demonstrate that the oscillatory solution cannot be well approximated by the corresponding non-oscillatory solution for the cases of large Dundurs’ index and external compressive force. Furthermore, it is found that both the thermoelastic effect and the inclined angle of the applied force have significant influences on the adhesive contact behaviors. The presence of temperature difference between contacting objects can either enhance or weaken the adhesion effect, which is related to the inclined angle of the external force. The results obtained from this paper may provide a new insight into the influence mechanism of the temperature on adhesion behaviors.

Cassette-like peeling system for testing the adhesion of soft-to-rigid assemblies

A novel cassette-like peeling system is developed to address the limitations of current peeling standards when evaluating bonding quality of soft-to-rigid assemblies. The system transforms the translation of a specimen in the conventional peeling configuration to rotation via a cassette-like spool clamping the specimen. The peeled film is loaded by tension to drive the winding of the spool, thus achieving self-similar crack propagation and a stationary peeling front unrelated to the stiffness of the film. These features enable the system’s compatibility with most universal testers and in situ observation of crack tip morphology with optical instruments. Analysis to derive the intrinsic fracture energy when peeling a soft film is conducted based on Griffith energy balance, making use of which, a parametric study is performed to clarify the related mechanisms. We carry out a comprehensive validation of the cassette-like peeling system by performing a series of peeling tests using our in-house prototype and by comparing the results with those from the conventional system. Owing to its universality and ease-of-use, the proposed cassette-like peeling system can potentially be applied to the development of the next generation of peel test standards.

Asymmetric non-slipping adhesion behavior of layered piezoelectric structures

Layered piezoelectric structures have found wide applications in micro-electro-mechanical systems (MEMS) due to their intrinsic electro-mechanical coupling effect. The adhesion effect resulting from various surface forces (e.g., the electrostatic force, capillary force, and Van der Waals force) has become one dominant factor in determining the reliability and service life of the MEMS devices. In this study, the asymmetric non-slipping adhesion behavior of layered piezoelectric structures under the action of different external loadings is investigated. A system of coupled singular integral equations are obtained for the stated problem in the framework of the generalized JKR theory, where the coupling effect between the normal and tangential contact stresses is taken into consideration. The closed-form analytical solutions of the electric displacement and stress fields within the contact zone are derived. The relations between the contact size and applied loadings are set up with the Griffith energy balance criterion. The effect of the mechanical and electric loads and the mismatch strain on the adhesion behavior of layered piezoelectric structures is discussed in detail. It is found that applying the electric load can only strengthen the adhesion effect for different types of layered piezoelectric structures. Both the inclined angle of the mechanical force and the geometric parameter of the contacting objects have significant effects on the adhesion behavior. The results obtained from present paper should be very useful for understanding the adhesion failure mechanism of the MEMS devices composed of layered piezoelectric structures.

Adhesive behavior of transversely isotropic piezoelectric bimaterials

The adhesive contact behavior between two dissimilar transversely isotropic piezoelectric cylinders is investigated in this paper. The effect of adhesion on the contact behavior between piezoelectric bimaterials is considered within the framework of the non-slipping JKR model, which takes the coupling effect between the tangential and normal tractions inside the contact region into account. The explicit analytical solutions of stress and electric displacement fields within the contact region are obtained by solving the resulting coupling singular integral equations with the analytical function theory. The relationship between the contact size and external loadings are established by adopting the Griffith energy balance criterion at the edges of the contact zone. It is found that different types of piezoelectric bimaterials show the same adhesive contact behaviors, which is different from the case of a single layer piezoelectric material. The result obtained from the present paper should be helpful for the design of micro-electro-mechanical systems (MEMS) devices involving multi-layered smart structures.

Theory of adhesive contact on multi-ferroic composite materials: Conical indenter

There is still a challenge to realize controllable attachment and detachment in the adhesive devices. New approaches of the controllable or reversible adhesion need to be developed in a wider area. In order to study the influence of the electric and magnetic quantities on the reversible adhesion, the adhesive contact problem between a half-space of the multi-ferroic composite material and a rigid conical indenter is investigated. The classical Johnson–Kendall–Roberts (JKR) and Maugis–Dugdale (MD) models are extended to the framework of magneto-electro-elasticity. The corresponding physical fields are analytically obtained. With the help of the Griffith energy balance relations, the stable equilibrium states of the adhesive contact are established. The corresponding indentation forces and the penetration depths for the JKR and MD models are derived in the closed-form. It is found that the pull-out forces associated with the JKR model depend on the electric potential and magnetic potential in certain cases. The validity is discussed by comparing the obtained solutions with the experimental data in the context of the elasticity. Numerical results show that the adhesive contact behaviors may be adjusted and controlled by changing the electric potential, the magnetic potential and the half apex angle of the rigid conical indenter. The present analytical results not only are the theoretical fundament for the forthcoming indentation experiments at the micro/nanoscopic scale, surface force microscopy (SFM) and atomic force microscopy (AFM), but also serve as guiding bionic design of the robots and grippers with reverse adhesion.

Controlling the adhesive pull-off force via the change of contact geometry

A first-order asymptotic analysis of the Griffith energy balance in the Johnson-Kendall-Roberts model of adhesive contact under non-symmetric perturbation of the contact geometry is presented. The pull-off force is evaluated in explicit form. A particular case of adhesive contact between a relatively stiff sphere and an elastic half-space is considered under the assumption that the sphere geometry is changed by the application of an arbitrary lateral normal surface loading. The effect of the sphere Poisson's ratio on controlling the adhesive pull-off force is considered. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction

We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.

Failure processes of cemented granular materials.

The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here we use a discrete element model simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular medium with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure, and compaction banding or anticracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow, and foam.

Molecular dynamics simulation of plastic deformation and interfacial delamination of NiTi/Ag bilayer by cyclic-nanoindentation: Effects of crystallographic orientation of substrate

This paper presents a comparative study of plasticity and fracture behavior of the NiTi/Ag bilayer for the different crystallographic orientations of the substrate. Molecular dynamic (MD) simulation was used to determine the deformation mechanism, dislocation density, plastic energy dissipation and delamination of the NiTi/Ag bilayers near the interface, when NiTi aligned at (1 0 0), (1 1 1), (1 1 0), (3 2 1), (2 1 0) and (2 1 1) faces during the cyclic-nanoindentation test. The Griffith energy balance model was used to estimate the energy release associated with the delamination. The results of the simulation are suggested the dependence of deformation mechanism, energy release rate (Gin), interfacial toughness (Kin) and average plastic energy dissipation per unit cycle (Eplastic) of NiTi/Ag bilayer on the crystallographic orientation of the NiTi substrate. Prismatic dislocation loop and the nest-like organization of the twins were responsible for the plastic deformation of the NiTi/Ag bilayers when NiTi aligned at (211,010,111) and (100,210,321) faces, respectively. The values of Gin and Kin of the bilayers were in the range of 64.27–147.71 J/m2 and 77–192 J/m2, respectively. The values of Eplastic is increased in the following order: NiTi (2 1 1) < NiTi (3 2 1) < NiTi (1 0 0) < NiTi (2 1 0) < NiTi (1 1 1) < NiTi (0 1 0). The average dislocation densities produced for the indenter radius of 30 Å were in the range of 1.23 × 1019–1.84 × 1019 m−2. The results show that the NiTi (0 1 0)/Ag case has the larger dislocation density than other bilayers. Both of hardness and the interfacial toughness of the NiTi/Ag at different crystallographic orientations were consistent with the free energy data obtained from Jarzynski’s equality for nanoindentation results, which were in the range of 3.35 × 10−4−7.81 × 10−4 eV/atom. Due to high interfacial toughness and hardness plus lower plastic energy dissipation, the NiTi (2 1 1)/Ag bilayer may show the better results for engineering and medical applications.

Visco- and plastoelastic fracture of nanoporous polymer sheets

We study the dependence of the fracture surface energy on the pulling velocity for nanoporous polypropylene (PP) sheets to identify two components: static and dynamic components. We show that these terms can be interpreted, respectively, as plastoelastic and viscoelastic components, as has been shown for soft polyethylene (PE) foams in previous work. Considering significant differences in the pore size, volume fraction, and Young’s modulus of the present PP and previous PE sheets, the present results suggest a universal physical mechanism for the fracture of porous polymer sheets. The simple physical interpretation emerging from the mechanism could be useful for developing tough polymers. Equivalence of Griffith's energy balance in fracture mechanics to a stress criterion is also discussed and demonstrated using the present experimental data. The dependence of the fracture surface energy on the stretching velocity for nanoporous polypropylene (PP) sheets was found to consists of static and dynamic components. These terms can be interpreted respectively as plastoelastic and viscoelastic components, as has been shown for soft polyethylene (PE) foams in a previous work. This simple physical interpretation suggests a universal mechanism for the fracture of porous polymer sheets, and could be useful for designing new tough polymers.

Theory of adhesive contact on multi-ferroic composite materials: Spherical indenter

This article is devoted to studying the adhesive contact problem for a spherical indenter on a half-space of the transversely isotropic multi-ferroic composite materials in a systematic manner. In view of magneto-electric properties of the spherical punch, four sets of mixed boundary value problems are taken into account. By virtue of the generalized potential theory method, the physical quantities on the contact surface, corresponding to the Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (MD) models, are explicitly obtained in the closed form. The expressions of indentation force and penetration depth associated with the Derjaguin-Muller-Toporov (DMT) model, which is the limiting case of the MD model, are derived through a limiting procedure. In particular, the analytical solutions to an external circular crack problem, which is new to literature, are presented as an auxiliary. Energy release rates pertinent to the JKR and MD models are derived and the corresponding equilibrium relations are established according to the Griffith energy balance. The adhesive contact behaviors including the pull-out force especially for three classical models are elaborated. The adjustment and control mechanism by the magnetic and electric means on adhesive contact behaviors is revealed. Numerical calculations are performed to present the obtained analytical results, compare the adhesive models and analyze the effect of magneto-electric properties on adhesive models. The obtained solutions are expected to be crucial to the forthcoming experiments on characterization of properties of multi-ferroic composite media, especially on the micro/nonoscopic scale.

The effect of ultrasonic impact treatment on the deformation behavior of commercially pure titanium under uniaxial tension

The deformation behavior of commercially pure titanium specimens subjected to surface hardening by ultrasonic impact treatment followed by uniaxial tension was investigated experimentally and numerically. The microstructure of the ultrasonically treated ~100μm thick surface layer undergoing uniaxial tension was revealed, using transmission electron microscopy and electron backscatter diffraction. Non-equiaxed 100–200nm α-Ti grains composed of 2nm diameter TiC and Ti2C nanoparticles, ω- and α″-phase crystallites were found in the 10μm thick uppermost layer. Fine and coarse α-Ti grains containing dislocations and twins were observed at depths of 20 and 50μm below the specimen surface, respectively. A non-crystallographic deformation (shear banding) mechanism at work in the nanostructured surface layer of the specimens under study was revealed. The evolution of shear bands was studied by the finite difference method, with the fine-grained structure being explicitly accounted for in the calculations. Shear band self-organization was described, using the energy balance approach similar to that based on Griffith's energy balance criterion for brittle fracture. The tensile deformation of the hardened layer lying at a depth of 50μm was implemented by the glide of dislocations and growth of deformation twins induced by preliminary ultrasonic impact treatment.

Lattice Approach in Continuum and Fracture Mechanics

This study reveals some aspects of lattice formulations to analyze the strain concentration of a famous classic problem in solid mechanics at two different mechanics perspectives: continuum and fracture. A 2D plane stress square panel with a single circular hole is discretized based on Voronoi tessellation. A superelliptic formulation is used to distribute lattice computational points over the panel. From the perspective of linear elasticity under uniaxial and biaxial loading, translational and rotational degrees-of-freedom are considered at each computational node of the lattice to obtain strain concentration factors (SCFs) around the circular perforation. It is observed that the lattice approach is able to approximate the elastic SCFs of three, four, and two in uniaxial, biaxial shear, and equibiaxial tension loadings, respectively. To study the linear elasticity and fracture mechanic (LEFM) and Griffith energy balance in uniaxial loading, a brittle lattice erosion technique is used to compute the energy release rate determined by change in the global stiffness matrix of the mesh with respect to crack extension. This fracture energy is then used to determine the mode I stress intensity factor of the crack emanating from the hole which is validated by the analytical formulation for the same problem. The comparison shows that both methods give very close results for the mode I stress intensity factor. Being simple in terms of constitutive formulation and failure criterion for erosion of brittle material, and also using a propagating crack extension approach, the lattice formulation is used to determine the fracture properties of cohesive/frictional material.

Effects of thickness and fibre misalignment on compression fracture in cross-ply (very) long cylindrical shells under external pressure

Combined effects of modal imperfections, transverse shear/normal deformation with/without reduced transverse shear modulus, G LT (caused by distributed fibre misalignments), on emergence of interlaminar shear crippling type instability modes, related to localization (onset of deformation softening), delocalization (onset of deformation hardening) and propagation of mode II compression fracture/damage, in thick imperfect cross-ply very long cylindrical shells (plane strain rings) under applied hydrostatic pressure, are investigated. Of special interest is the question: what are the geometric and/or material parameters that induce localized and delocalized states in imperfect cross-ply (very) long cylindrical shells under hydrostatic compression simultaneously, and what would be the consequences of such occurrences? The primary accomplishment is the (hitherto unavailable) computation of the layer-wise mode II stress intensity factor, energy release rate and kink–crack bandwidth, under hydrostatic compression, from a nonlinear finite-element analysis, using Maxwell's construction and Griffith's energy balance approach. Additionally, the shear crippling angles in the layers are determined using an analysis, pertaining to the elastic inextensional deformation of the compressed (plane strain) ring. Numerical results include effects of (i) thickness-induced transverse shear/normal deformation and (ii) uniformly distributed fibre misalignments, on localization and delocalization, and consequently on compression fracture/damage characteristics of thick imperfect cross-ply very long cylindrical shells.