Kink Band Propagation Research Articles

Computational analysis of the failure mechanisms of a laminated composite in double-edge notch compression configuration

This manuscript presents a combined experimental–computational investigation of the compression failure response of laminated composites in double-edge notch compression (DENC) configuration. Analysis of in-situ and post-test DENC experiment results indicates the presence of multiple failure mechanisms, including ply splitting, delamination, and compression kink bands. In order to characterize the onset, growth, and interplay of the critical and subcritical damage mechanisms, a multiscale progressive damage analysis approach is implemented. A nonlocal multiscale damage model explicitly tracks the intraply failure mechanisms that lead to the formation and propagation of kink bands in the specimen. A cohesive zone model is used to track initiation and progression of ply splitting in the specimen. The splitting model was implemented using implicit finite element simulations and deployed with a pre-crack insertion technique to reduce simulation time while preserving prediction accuracy. Model parameters are calibrated based on available calibration data and measurements. The effects of split location and growth characteristics on model predictions are studied. The computational model along with a suite of experiments were employed to study the formation, growth and interactions of damage mechanisms in the composite specimens subjected to compression loading. The onset of matrix damage is not clear from the experimental images but the model predicts early onset around the onset time of splits which greatly reduce the stress concentration at the notches. Analysis of acoustic emission energy experimental data indicate that observable compression failure mechanisms are not causing nonlinearity consistently exhibited in the experiment responses. Simulation results demonstrate the capability of the multiscale modeling approach to predict critical kink bands and sub-critical matrix cracking and splitting in the DENC specimens while reducing computational cost compared to a direct numerical simulation of fibers and matrix.

Kinking in a refractory TiZrHfNb0.7 medium-entropy alloy

As a type of cooperative deformation like twinning, kinking can improve the deformability of materials by stress relaxation and crystal reorientation. In this work, kinking with 〈0 1 1〉 lattice rotation axis was identified in a refractory TiZrHfNb0.7 medium-entropy alloy (MEA). Through intragranular misorientation axis (IGMA) analysis, the {1 1 2} 〈1 1 1〉 dislocation slip was determined. The formation of intensive band structure in 70% cold rolled alloy was attributed to continuous nucleation and propagation of kink bands in coarse grains.

Steady-State Kink Band Propagation in Layered Materials

Failure by steady-state kink band propagation in layered materials is analyzed using three substantially different models. A finite element model and an analytical model are developed and used together with a previously introduced constitutive model. A novel methodology for simulating an infinite kink band is used for the finite element model using periodic boundary conditions on a skewed mesh. The developed analytical model results in a transcendental equation for the steady-state kink band propagation state. The three models are mutually in good agreement and results obtained using the models correlate well with the previous experimental findings.

Inverse method for estimation of composite kink-band toughness from open-hole compression strength data

Fiber-reinforced polymer matrix composite materials can fail by kink-band propagation mechanism when subjected to in-plane compressive loading. This mode of failure is especially prevalent in compressive loading of laminates with holes, cut-outs, or impact damage. Most of the successful models for predicting compressive strength of such laminates require “fracture” toughness associated with kink-band propagation under in-plane compression. However, this property is difficult to measure experimentally, limiting the use of such models in design practice. In this paper an inverse method is proposed to estimate the kink-band toughness of the laminate from its open-hole compression strength data, which is an easier property to measure experimentally. Furthermore, a scaling relationship is proposed to estimate kink-band toughness for other laminate configurations of the same material. Through various investigations, it is shown that the developed inverse method and scaling relationships can serve as effective and accurate tools in the prediction of open-hole compression and compression after impact strengths for multiple layups of different material systems.

Strain fields induced by kink band propagation in Cu-Nb nanolaminate composites

Kink band formation is a common deformation mode for anisotropic materials and has been observed in polymer matrix fiber composites, single crystals, geological formations, and recently in metallic nanolaminates. While numerous studies have been devoted to kink band formation, the majority do not consider the often rapid and unstable process of kink band propagation. Here we take advantage of stable kink band formation in Cu-Nb nanolaminates to quantitatively map the local strain fields surrounding a propagating kink band during uniaxial compression. Kink bands are observed to initiate at specimen edges, propagate across the sample during a rising global stress, and induce extended strain fields in the non-kinked material surrounding the propagating kink band. It is proposed that these stress/strain fields significantly contribute to the total energy dissipated during kinking and, analogous to crack tip stress/strain fields, influence the direction of kink propagation and therefore the kink band inclination angle.

Compressive failure of UD-CFRP containing void defects: In situ SEM microanalysis

Here we present an in situ scanning electron microscopy (SEM) investigation of the compressive failure of unidirectional (UD) carbon fibre reinforced polymer (CFRP) composites with varying pre-existing void content. The experiments were carried out within a dual beam microscope, which couples a SEM with a focused ion beam (FIB), allowing sub-surface investigations of damage. In these tests, the specimen is monitored during the entire loading history, allowing the correlation of microstructural changes and the evolving load–displacement behaviour. Therefore, loading characteristics can be linked directly to failure events. Observations of the sequence of events leading to failure showed direct fibre deflection into a kinked shape eventually followed by fibre fracture. Failure of void-containing CFRP was shown to depend on the void shape as well as the proximity of the void to the kink band. In some cases voids stopped the propagation of kink bands, while in other cases the void caused the kink to deflect in a new direction. The failure structure was observed to change with time, both during hold-load segments as well as after unloading. Through cross-sectional ion beam milling in the unloaded state, the sub-surface damage was observed and shown to be similar to that observed at the surface.

A micromechanical model for kink-band formation: Part I — Experimental study and numerical modelling

The initiation and propagation of kink-bands are investigated through an experimental study and numerical modelling. Based on the results achieved, the sequence of events and key features for kink-band formation are identified; particularly, matrix yielding is found to play a crucial role in the process, and fibres are found to fail in the compressive side first. The findings from both the experimental and numerical programmes show a remarkable agreement, and are further applied to the development of an analytical model ( Part II of this paper) for kink-band formation.

Size Effect on Compressive Strength of Sandwich Panels with Fracture of Woven Laminate Facesheet

Prismatic sandwich specimens of various sizes, geometrically scaled in the ratio 1:2:4:8, are subjected to eccentric axial compression and tested to failure. The sandwich core consists of a closed-cell polyvinyl chloride foam, and the facesheets are woven glass-epoxy laminates, scaled by increasing the number of plies. The test results reveal a size effect on the mean nominal strength, which is strong enough to require consideration in design. The size effect observed is fitted with the size effect law of the energetic (deterministic) size effect theory. However, because of inevitable scatter and limited testing range, the precise form of the energetic size effect law to describe the test results is not unambiguous. The Weibull-type statistical size effect on the mean strength is ruled out because the specimens had small notches which caused the failure to occur in only one place in the specimen, and also because the observed failure mode was kink band propagation, previously shown to cause energetic size effect. Various fallacies in previous applications of Weibull theory to composites are also pointed out.

Kink band propagation in layered structures

Confined layered structures in layer-parallel compression exhibit kink band deformation that has an associated severe initial instability. However, once the first kink band forms the system restabilizes and the bands then propagate in two mechanisms: band broadening and band progression. Previous work on triggering the initial instability and band broadening is now extended to include band progression. A new model for this propagation mechanism that successfully accounts for the modulating restabilizing response is presented and quantitative comparisons with the physical experiments yield excellent results.

Eigenvalue method for computing size effect of cohesive cracks with residual stress, with application to kink-bands in composites

The previously developed eigenvalue method for computing the size effect of cohesive crack model is extended to the cohesive crack model with a finite residual stress. In this model, the structure size for which a specified relative length of kink-band corresponds to the maximum load is obtained as an eigenvalue of a homogeneous Fredholm integral equation. This new method is direct and much more efficient than the classical finite element approach in which the entire load-deflection history must be computed to obtain the maximum load. A secondary purpose of the paper is to apply the new method to the effect of structure size on the compressive strength of unidirectional fiber–polymer composites failing by propagation of kink-band with fiber microbuckling. The kink-band is simulated by a cohesive crack model with a linear compressive softening law and a finite residual stress. The simulation shows that the specimens tested have a negative–positive geometry, i.e., the energy release rate of the kink-band for a unit load first decreases but at a certain length of propagation begins to increase. Finally the effect of shape of the softening law of cohesive crack on the size effect curve is studied by using the new eigenvalue method. It is shown that, for a negative–positive geometry, the size effect on the peak load depends on the entire softening curve if the specimens is not too small.

On the axial propagation of kink bands in fiber composites : Part ii analysis

A new micromechanical model is presented to simulate the steady-state axial propagation of kink bands investigated experimentally in the accompanying paper (Part I) . The fibers are in a hexagonal array and are assumed to be isotropic and linearly elastic, while the matrix is modeled as an elastic-powerlaw viscoplastic solid. Matrix properties for the model are determined from shear tests on the composite and compression tests on neat PEEK. The model is used to predict the propagation stress (σP) of the AS4⧹PEEK composite and to investigate the sensitivity of σP to band inclination, matrix properties, and loading rate. A simple model recently reported in the literature is calibrated to the current material system and compared with the present experimental data and model predictions. The micromechanical model is found to predict the propagation stress reasonably well and to capture the rate dependence of the composite. The simple model is found to capture the trends of the behavior.

On the axial propagation of kink bands in fiber composites : Part i experiments

In many fiber composites, longitudinal compressive failure leads to the formation of kink bands. It has been found that these kink bands, once formed, can be made to propagate (broaden) in a steady-state manner at a constant stress level called the propagation stress (σP) . This is a characteristic stress of the material which, for the AS4⧹PEEK composite used in the study reported here, is approximately 40% of its compressive strength. This phenomenon is investigated experimentally using a special confining set-up that allows direct observation of the propagation process. For the composite studied, the kink bands have a repeatable inclination (β) of approximately 15°, and the fibers within the bands are rotated to about 30° in the absence of a load. When loaded to σP, however, they are found to rotate further to 40°, that is, substantially greater than the 2β reported elsewhere. The mechanism of propagation is found to be a bend-break-rotate sequence undergone by short segments of fibers at the edge of the kink band. It is well known that polymeric matrix composites such as the one used in this study exhibit rate-dependent behavior. Experimental results are presented which show that the kink band propagation stress is also rate dependent.

On kink-band propagation in fiber composites

Two kinds of kink-band propagation in the compression of aligned-fiber composites are studied analytically : band broadening, discovered experimentally by Moran, Liu and Shih, 1996, in which a uniform kink band grows in the direction of loading at constant stress under increasing deformation; and transverse kink propagation, in which a kink band traverses a specimen quasi-statically under constant overall shortening. The analysis is based on a 1-D, geometrically nonlinear couple-stress theory of composite kinking that takes elastic fiber bending resistance into account together with idealized nonlinear stress–strain relations, but assumes non-breaking fibers. Simple results for the band-broadening and transverse propagation stresses are deduced, and their significance is discussed.

Kink band propagation and broadening in ductile matrix fiber composites: Experiments and analysis

Experimental observations of the kinking process in ductile matrix fiber composites confirm that kinking occurs in three distinct stages, incipient kinking, transient kinking and band broadening. Each of these stages is controlled by different kinematics. These stages and their underlying kinematics are described in detail in terms of soft deformation modes. New features revealed by our micrographs and experiments include: the tip of a propagating band lies at a shallower angle than the rest of the band, band broadening is steady-state phenomenon and occurs through localized micro-kink gliding. The experimentally measured steady-state band broadening stress is in agreement with a previous analytical prediction.

Initiation and axial propagation of kink bands in fiber composites

The failure of fiber-reinforced composites in compression is sudden, uncontrolled and results in the dynamic formation of narrow zones of inclined kinked fibers and in a drastic reduction in load bearing capacity. Experimental results are presented which demonstrate that such materials do maintain significant post-failure strength and “ductility.” Following the onset of failure, kink bands which were initiated dynamically could be made to propagate (broaden) in the fiber direction. Under displacement controlled loading, the propagation of the bands takes place in a steady-state manner. In the case of the APC-2/AS4 composite analyzed, quasi-static propagation of this failure took place at a stress level which was 40% of the strength of the intact material. The propagation of the band involved progressive addition of narrow zones of fibers from the adjacent intact material by rotation and breaking. This new characteristic stress of such materials has been called propagation stress. Several requirements and guidelines for establishing the true value of this material property, free of influence from experimental conditions and specimen geometry, are outlined.

Stress Singularity due to Kink Band Weakening a Unidirectional Composite under Compression

A Williams type of eigenfunction expansion approach is used to compute the local stress singularity representing a measure of the degree of inherent flaw sensitivity of unidirectional fiber reinforced composites subjected to compression. Previous experimental studies have qualitatively linked the formation of kink bands to the presence of fabrication defects, such as fiber misalignment. These local singular stress regions serve as the primary trigger mechanism for kink band propagation in 0°-plies. The present analysis also explains the previous test results relating to propagation of failure from a notch in a unidirectional composite under compression. Furthermore, the present investigation is the first to quantify, in the context of LEFM (linear elastic fracture mechanics), the sensitivity of these composites to inherent local flaws, such as fiber misalignments, and also shows the inadequacy of the conventional elastic micro-buckling type of analysis to fully explain the experimental results. Although because of the assumed isotropy of the fiber and matrix materials, the present study is primarily suited to glass fiber reinforced composites, the conclusions drawn here are general enough to apply to carbon fiber reinforced composites as well. Numerical results presented include the effects of fiber included wedge angle, and the ratios of fiber-matrix shear moduli and Poisson's ratios on the strengths of the mode I and mode II singularities. Of special practical interest is the present LEFM type of analysis applied to quantitatively investigate the inherent flaw sensitivity of two E-glass/epoxy composites experimentally investigated earlier. Compression fracture type of failure of these composites can be fully explained and quantified by the present two-dimensional LEFM-based method, which is beyond the scope of one-dimensional micro-buckling approach.

Analytical/Experimental Evaluation of Hybrid Commingled Carbon/Glass/Epoxy Thick-Section Composites under Compression

This paper outlines a current effort at improving the compressive strength of carbon fiber reinforced composites (CFRC) by using a hybrid carbon/glass commingling concept. Prior investigations into the hydrostatic strength of thick-section carbon fiber reinforced composite cylinders resulted in failures which were significantly lower (50 to 70% of design pressure) than anticipated. The formation and propagation of fiber kink bands at the microscopic level, triggered by the fiber misalignment defects formed during the manufacturing process, leading to a shear crippling failure at the macroscopic level is the dominant compressive failure mode in the presence of fiber misalignment or waviness. It is theorized that one way to improve compressive strength is through the use of a commingled (at the tow level) hybrid fiber system. A novel fracture mechanics based concept for commingling a small percentage of glass with carbon fibers to suppress compressive failures due to inelastic micro-buckling of fibers and kink band propagation is developed. A Griffith type fracture criterion for a mode II crack growth, based on the principle of energy balance, is introduced to derive the hitherto unknown concept of kink toughness (i.e., resistance to kink band propagation), and to determine the required glass-carbon ratio for possible enhancement of toughness against the kink band propagation. The width of a kink band normalized with respect to a characteristic length scale, such as thickness of a matrix impregnated fiber tow can be used as a practical measure for kink toughness. Preliminary experimental data suggest enhancement of the compressive and flexural strengths of the composite material even with a small percentage (15%) of glass fibers in commingled hybrid composites. Most significantly, inspection of the failed compression test coupons clearly demonstrates that introduction of this small percentage of glass fibers is effective in changing the failure mode away from the catastrophic kink band failure mode. Furthermore, it may be noted that the flexural hybrid commingled glass/carbon/epoxy composite specimens have failed in tension, which is in sharp contrast to what has been observed in their baseline carbon/epoxy counterparts.

Geometry and Loading Effects on the Compressive Strength of Fibrous Composites

This work addresses the important engineering problem of the com pressive strength of fibrous laminated composites, bridging the micromechanics relevant to compressive failure due to fiber kinking with the global characteristics of a composite structure Simple modeling incorporates the influence of boundary conditions, laminate thickness and layup configuration, as well as the importance of the microgeometry. The mechanism of failure under compression is assumed to be microbuckling of fibers that localizes at points with the maximum initial imperfection and leads to the formation and, under critical conditions, propagation of kink bands. To analyze the mechanics of kinking and to calculate the critical compressive stress, a steady state kink propagation model is utilized for the layers under compression in the fiber direction. The analysis results are used to gain a better understanding of the influence of the macrogeometry (laminate thick ness and gauge length) in addition to the microgeometry (fiber diameter and fiber volume fraction), and the fiber and matrix material properties The predictions of the model are compared with experimental results for carbon/thermoplastic unidirectional laminates under direct compression and cross-ply laminates under four-point bending.