Model For Compressive Failure Research Articles

A micro-macro constitutive model for compressive failure of rock by using 4D lattice spring model

In this work, a micro-macro mechanics-based constitutive model is developed to describe the compressive failure process of rock. A micromechanics model is first developed based on the conceptual model of a micro cracked spring bond, where two micro parameters with clearly geometric meanings are introduced. By using the micromechanics model, it is possible to reproduce the whole nonlinear failure process of the rock under compressive loading, however, it fails to predict the reasonable quantitative relation between the crack initiation stress (σCI) and the direct tensile strength (DTS) that is commonly observed in laboratory tests. Therefore, a macroscopic failure criterion is introduced to determine the failure state of the spring bond instead of the spring deformation used in the micromechanics model. The numerical results indicate that the 4D-LSM with the micro-macro constitutive model can not only fully reproduce the whole nonlinear behavior of rock under different confining pressures, but also reproduce the quantitative relation between σCI and the DTS and the overall macroscopic nonlinear failure strength criterion defined by Hoek and Brown. The micro-macro constitutive model not only provides a feasible solution for better describing the complex nonlinear compressive failure process of rock but helps to better understand the internal failure mechanism of rock.

Development of a compressive failure model for carbon fiber composites and associated uncertainties

An approach to increase the value of carbon fiber for wind turbines blades, and other compressive strength driven designs, is to identify pathways to increase its cost-specific compressive strength. A finite element model has been developed to evaluate the predictiveness of current finite element methods and to lay groundwork for future studies that focus on improving the cost-specific compressive strength. Parametric studies are conducted to understand which uncertainties in the model inputs have the greatest impact on compressive strength predictions. A statistical approach is also presented that enables the micromechanical model, which is deterministic, to efficiently account for statistical variability in the fiber misalignment present in composite materials; especially if the results from the hexagonal and square pack models are averaged. The model was found to agree well with experimental results for a Zoltek PX-35 pultrusion. The sensitivity studies suggest that the fiber packing and the interface shear strength have the greatest impact on compressive strength prediction for the fiber reinforced polymer studied here. Based on the performance of the modeling approach presented in this work, it is deemed sufficient for future work which will seek to identify carbon fiber composites with improved cost-specific compressive strength.

Hypervelocity impacts into porous graphite: experiments and simulations.

We present experiments and numerical simulations of hypervelocity impacts of 0.5 mm steel spheres into graphite, for velocities ranging between 1100 and 4500 m s-1 Experiments have evidenced that, after a particular striking velocity, depth of penetration no longer increases but decreases. Moreover, the projectile is observed to be trapped below the crater surface. Using numerical simulations, we show how this experimental result can be related to both materials, yield strength. A Johnson-Cook model is developed for the steel projectile, based on the literature data. A simple model is proposed for the graphite yield strength, including a piecewise pressure dependence of the Drucker-Prager form, which coefficients have been chosen to reproduce the projectile penetration depth. Comparisons between experiments and simulations are presented and discussed. The damage properties of both materials are also considered, by using a threshold on the first principal stress as a tensile failure criterion. An additional compressive failure model is also used for graphite when the equivalent strain reaches a maximum value. We show that the experimental crater diameter is directly related to the graphite spall strength. Uncertainties on the target yield stress and failure strength are estimated.This article is part of the themed issue 'Experimental testing and modelling of brittle materials at high strain rates'.

Compressive failure mechanism and strength of unidirectional thermoplastic composites based on modified kink band model

A modified kink band model for compressive failure in fiber direction of fiber reinforced composite polymers was investigated and established in this study. Practically modifying the previous kink band model by logically applying a quadratic yield function combining transverse tensile and shear stress to the kinking instability, the modified model was able to determine the compressive strength along with the kink band failure angle theoretically. Especially in case of unidirectional carbon fiber reinforced thermoplastic composites, the compressive test procedure the authors have developed and its results revealed that the kink band failed in out-of-plane direction with each different inclined angle depending on temperature. From the correlation of the observed kink band failure angle and the evaluated compressive strength affected by temperature condition, the modified kink band failure formula was validated.

Compressive failure model for brittle rocks by shear faulting and its evolution of strength components

A physical theory for brittle failure is presented that aims to explain both the phenomenological and micro-structural observations. The objective of this model is to capture the important attributes inferred from micro-structural experiments so as to arrive at constitutive relations that describe macroscopic failure behaviour. Based on experimental results, the micromechanical failure characterisation is summarised first. The localised failure process of rock will experience two stages: the brittle breakage stage (bond rupture of rock bridge) and the sliding stage (frictional resistance of failure plane mobilisation). A physical model is developed by dividing the sample into elastic and localised shear zones. Furthermore, the deformation process of the localised shear zone is divided into bond loss and frictional resistance mobilisation in two stages. To combine the micro-characteristics with the macromechanical properties, the chain models in localised shear zone, and the homogenisation method are adopted. The model is validated against the experimental data of Yumlu and Ozbay's. Subsequently, the localised progressive failure characteristics of rock are analysed by changing the model's parameters. The intrinsic effects and influential factors such as geometrical effects (size effect, shape effect), the strain softening phenomenon and Class II stress–strain curves are revealed. Finally, in order to be used easily by engineers, the simplified description of rock failure process and its evolution of strength components are given based on the model.

Investigation of fused silica dynamic behaviour

The survivability of the fused silica shields to shrapnel impacts is a key factor for the affordable operation of the intense laser irradiation future facility Laser Mega Joule (CEA-CESTA). This paper presents experimental data and computational modelling for LMJ fused silica upon shock wave loading and unloading. Gas-gun flyer plate impact and explosively driven tests have been conducted to investigate the dynamic behaviour of this material. Hugoniot states and the Hugoniot Elastic Limit of LMJ fused silica have been obtained. These experimental data are useful for determining some constitutive model constants of the Crack-Model, a continuum tensile and compressive failure model with friction based on Rubin M. B. and Attia A. V.'s work. This model has been improved by taking into account nonlinear elasticity. The numerical results obtained by performing computations of the previous tests and some ballistic impact tests are discussed. Further developments to simulate the permanent densification and the solid-to-solid phase transformation of fused silica are required.

Compressive failure model for fiber composites by kink band initiation from obliquely aligned, shear-dislocated fiber breaks

Predicting compressive failure of a unidirectional fibrous composite is a longstanding and challenging problem that we study from a new perspective. Motivated by previous modelling of tensile failure as well as experimental observations on compressive failures in single carbon fibers, we develop a new micromechanical model for the compressive failure process in unidirectional, planar composites. As the compressive load is increased, random fiber failures are assumed to occur due to statistically distributed flaws, analogous to what occurs in tension. These breaks are often shear-mode failures with slanted surfaces that induce shear dislocations, especially when they occur in small groups aligned obliquely. Our model includes interactions of dislocated and neighboring intact fibers through a system of fourth-order, differential equations governing transverse deformation, and also allows for local matrix plastic yielding and debonding from the fiber near and within the dislocation arrays. Using the Discrete Fourier Transform method, we find a ‘building-block’ analytical solution form, which naturally embodies local length scales of fiber microbuckling and instability. Based on the influence function, superposition approach, a computationally efficient scheme is developed to model the evolution of fiber and matrix stresses. Under increasing compressive strain the simulations show that matrix yielding and debonding crucially lead to large increases in bending strains in fibers next to small groups of obliquely aligned, dislocated breaks. From the paired locations of maximum fiber bending in flanking fibers, the triggering of an unstable kink band becomes realistic. The geometric features of the kink band, such as the fragment lengths and orientation angles, will depend on the fiber and matrix mechanical and geometric properties. In carbon fiber–polymer matrix systems our model predicts a much lower compressive failure stress than obtained from Rosen’s classic microbuckling model, yielding values much closer to those observed experimentally.

A Micromechanics-Based Finite Element Model for Compressive Failure of Notched Uniply Composite Laminates Under Remote Biaxial Loads

A micromechanics based failure initiation predictive capability for analyzing notched composite laminates loaded remotely in multiaxial compression is reported. The model relies on the results from a previous experimental study that investigated compression failure mechanisms in special “uniply” composite laminates. The finite element method (FEM) was used in the solution process. The experimental results showed that the dominant mode of failure initiation was kink banding near the hole edge. The kink band was confined in extent to a distance within one half of the hole radius. The fibers within the kink band were rotated both in plane and out of the plane of the laminate. The position of the kink band with respect to the center of the notch depended on the remote biaxial load ration. In the FEM, the region in which kink banding takes place is contained within a finite size rectangular area, and is meshed as an alternatingly stacked region of fiber and matrix layers. The values of boundary loads on this rectangular area which correspond to kink banding is related to the remotely applied loads via an available closed form analysis for orthotropic laminates. Good agreement is found between experiment and analysis for a wide range of notch sizes.

A Micromechanics Model for Compressive Failure of Unidirectional Fibre-Reinforced Plastics

In this paper a method is presented for predicting the compressive strength of unidirectional fibre-reinforced plastics. Initial fibre misalignment and nonlinear shear response are included in the model which is based on a combination of other published methods. Predictions are shown to compare well with test data from an improved test method for carbon fibre-reinforced materials; one with an epoxy matrix and one with a PEEK matrix. Acceptable predictions are shown to depend on an appropriate assessment for fibre misalignment. The influence on compressive strength of moisture uptake by the composite was seen to be correctly predicted by the model.

Compressive failure model for anisotropic plates with a cutout

Compressive failure model for anisotropic plates with a cutout

Two-Dimensional Modelling of Compressive Failure in Delaminated Laminates

An analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites.