Point Impact Load Research Articles

Micromechanics of impact damage of ductile (ZnS) and hard (MgAl2O4) ceramics

AbstractThe time‐resolved generation of the electromagnetic emission (EME) and acoustic emission (AE) excited by the point impact loading of ductile ZnS and hard MgAl2O4 ceramics was detected. It has been found that the EME generation precedes the AE activity in loaded ZnS ceramics, while the EME signal lags the AE generation from MgAl2O4. This dissimilarity of temporal patterns was explained by the difference between the mechanisms of the excitation of electrical charges in loaded ductile and hard ceramics. The EME from loaded ZnS is caused by the motion of charged dislocations, while, the EME effect in MgAl2O4 is due to the annihilation of opposite electric charges emerged on microcrack edges. The AE energy yield from growing microcracks in both ceramics as well as the EME activity in MgAl2O4 were found to be random (Poissonian‐like), which is typical of the localized fracture of solids occurring without long‐range interactions between perturbed structural localities. The energy distribution in EME time series generated in ductile ZnS prior to cracking followed a power law, which is characteristic for the correlated motion of charged dislocations at the stage of plastic flow. The temporal patterns of damage accumulation at different structural levels were specified through physical and mechanical properties of tested materials.

Crack nucleation and growth during dynamic indentation of chemically-strengthened glass

Dynamic point impact loading is a primary cause of fracture of glass screens on mobile devices. An improved understanding of crack initiation and evolution under high-speed indentation could contribute to the development of materials with better performance, but experimental observations are challenging due to the short timescales and limited depth-of-field of optical microscopy. To address this need, we have observed fracture of a chemically-strengthened glass during dynamic indentation using in situ x-ray phase-contrast imaging (XPCI). Median cracks initiate below the surface of the glass, at a depth approximately corresponding to the depth at which the surface residual compressive stress diminishes to zero. These cracks initially propagate at ∼10ms−1, rapidly accelerating to >100ms−1. We also observe some evidence for rate-dependent behavior, in that indentation at the lowest rates studied here (below about ∼0.15ms−1) fails to initiate cracks regardless of the depth of the indentation (up to 18μm), while indentation at higher rates produces median cracks that either arrest or cause complete fracture, depending on the depth of indentation.

Impact energy distribution and wavefront shape in granular material assemblies

In this study, we investigated the dynamic response of granular materials subjected to point impact loading based on the discrete element method. The average velocity of the stress pulse was defined. The effect of elastic modulus on wave velocity was analyzed. The energy diffusion process in granular materials is affected by the contact between the particles, which is mainly reflected in two aspects: contact distribution and force transmission ratio. We first compared the wavefront shape in the specimens with different particle arrangements, and then assigned different material properties to the matrix particles. The wavefront shape is consistent with the previous results which proved the influence of the force transmission ratio. Finally, the variations of particle acceleration, kinetic energy and wave velocity at different impact angles are discussed. Our research reveals the energy propagation process through the contact between particles within granular materials. Our research results can be a reference for material design using granular materials for energy collection, energy absorbing etc.

The addition of synthetic fibres to concrete to improve impact/ballistic toughness

Concrete is relatively weak in tension and may require some form of reinforcement to cope with tensile forces. Steel reinforcing bar is often used to cater for tensile and compressive forces. However, current research shows that the use of steel reinforcing bar does not afford concrete protection against impact. Alternatively it has been shown that where fibres are added to concrete mixes protection is afforded through increased energy absorption. It would appear that the dispersion of fibres throughout a concrete mix affords a degree of toughness between the reinforcement bar spacing.This research investigates the use of Type 1 micro synthetic fibres, Type 2 macro synthetic fibres and steel fibres used as post crack reinforcement in concrete samples when subject to a variety of stress induced states and compares the performance of these fibre mixes to that of a plain concrete mix. The test programme adopted, subjected cube specimens to compressive strength tests, beam samples to both three point flexural bending and single point impact loading, and concrete slab sections to shot gun fire. The parameters investigated under test were: compressive strength, flexural strength, load deflection analysis, energy absorption and impact performance/resistance. Modelling the impact of shot fire on the test specimens was carried out using Finite Element Analysis, to inform slab design. The results of this investigation are of particular significance to the resilience of concrete structures under terrorist attack.The results show that the adoption of Type 2 macro synthetic fibres as concrete post crack reinforcement provide the greatest toughness when compared with the other fibre types and offer the greatest protection from spalling of the back face of the concrete slab, being the main consideration with regard to the performance of the slab on testing with shotgun fire. Damage containment after ballistic testing was also noted where Type 2 fibres were used. The Finite Element Analysis models were successful at predicting the damage recorded to the concrete slabs, when subject to the shotgun fire performance test.

Matrix crack interacting with a delamination in an impacted sandwich composite beam

Delamination interacting with matrix cracking is a characteristic failure mechanism that is observed in the damage evolution of laminated composites subjected to low velocity impact. This failure mode can be studied in isolation by investigating the low velocity impact response of sandwich panels that have thin face sheets bonded to a core. In these panels, failure is seen to initiate in the core (akin to the matrix) by cracking, leading to delamination between the core and the face sheet. Experimental and modeling results for the flexural response and failure mechanisms of sandwich composite beams under three point bend loading, both for quasi-static and impact loading are presented. Digital image correlation (DIC) technique is used to obtain the surface strain field during the response event as well as capturing the onset of failure. A 2D, plane strain finite element (FE) model using the Smeared Crack Approach (SCA) has been developed to predict the response, and to capture the interactive failure seen in the experiments. The FE model accurately captures the response seen in the experiments as well as the mode of failure and the progression.

Experimental impact damage study of a z-pinned foam core sandwich composite

This paper assesses the impact damage and post-impact compression properties of a foam core sandwich composite reinforced with through-thickness z-pins. Low-speed flat-wise compression tests performed on the sandwich composite revealed that z-pins improved the elastic modulus, crush strength and absorbed energy capacity (by 260–300%). However, these property improvements do not necessarily translate into a reduction in the amount of damage suffered by the z-pinned sandwich composite under localised (point) impact loading. There was no reduction to the impact damage area or an improvement to the post-impact compression properties of the z-pinned sandwich composite at low-impact energies (when damage was confined to the impacted face skin). Z-pins were only marginally effective at reducing the impact damage when the impact energy was high enough to cause core crushing. Z-pins absorbed high-impact energy via splitting, microbuckling and fragmentation during core crushing which reduced slightly the amount of impact damage to the sandwich composite. However, this did not cause a significant improvement to the post-impact compressive stiffness and strength for most energy levels.

Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.

Wave propagation and transient response of functionally graded material circular plates under a point impact load

Wave propagation and transient response of an infinite functionally graded circular plate under a point impact load are studied. The effective material properties are assumed to vary as a power form of the thickness coordinate. Considering the effects of transverse shear deformation and rotary inertia, the governing equations and analytic dispersion relation of the plate are obtained. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load are obtained. The influence of volume fraction distributions on wave propagation and transient response of functionally graded plates is discussed in detail.

Wave propagation and transient response of a FGM plate under a point impact load based on higher-order shear deformation theory

Abstract In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load are presented. The effective material properties of functionally graded materials (FGMs) for the plate are assumed to vary continuously through the plate thickness and be distributed according to a volume fraction power law along the plate thickness. Based on the higher-order shear deformation theory and considering the effect of the rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived by using the Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Then, using the dispersion relation and integral transforms, exact integral solutions for the functionally graded plate under a point impact load are obtained. The transient response curves of the functionally graded plates are plotted and the influence of volume fraction distributions on transient response of functionally graded plates is analyzed. Finally, the solutions of the higher-order shear deformation theory and the first-order shear deformation theory are studied.

Homogenized rigid-plastic model for masonry walls subjected to impact

A simple rigid-plastic homogenization model for the analysis of masonry structures subjected to out-of-plane impact loads is presented. The objective is to propose a model characterized by a few material parameters, numerically inexpensive and very stable. Bricks and mortar joints are assumed rigid perfectly plastic and obeying an associated flow rule. In order to take into account the effect of brickwork texture, out-of-plane anisotropic masonry failure surfaces are obtained by means of a limit analysis approach, in which the unit cell is sub-divided into a fixed number of sub-domains and layers along the thickness. A polynomial representation of micro-stress tensor components is utilized inside each sub-domain, assuring both stress tensor admissibility on a regular grid of points and continuity of the stress vector at the interfaces between contiguous sub-domains. Limited strength (frictional failure with compressive cap and tension cut-off) of brick-mortar interfaces is also considered in the model, thus allowing the reproduction of elementary cell failures due to the possible insufficient resistance of the bond between units and joints. Triangular Kirchhoff-Love elements with linear interpolation of the displacement field and constant moment within each element are used at a structural level. In this framework, a simple quadratic programming problem is obtained to analyze entire walls subjected to impacts. In order to test the capabilities of the approach proposed, two examples of technical interest are discussed, namely a running bond masonry wall constrained at three edges and subjected to a point impact load and a masonry square plate constrained at four edges and subjected to a distributed dynamic pressure simulating an air-blast. Only for the first example, numerical and experimental data are available, whereas for the second example insufficient information is at disposal from the literature. Comparisons with standard elastic–plastic procedures conducted by means of commercial FE codes are also provided. Despite the obvious approximations and limitations connected to the utilization of a rigid-plastic model for masonry, the approach proposed seems able to provide results in agreement with alternative expensive numerical elasto-plastic approaches, but requiring only negligible processing time. Therefore, the proposed simple tool can be used (in addition to more sophisticated but expensive non-linear procedures) by practitioners to have a fast estimation of masonry behavior subjected to impact.

Modelling of low velocity impact damage in Laminated Composites

In this study a simple model is developed that predicts impact damage in a composite laminate avoiding the need of the time-consuming dynamic finite element method (FEM). The analytical model uses a non-linear approximation method (Rayleigh-Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point impact load at its centre. It is assumed that the deformation due to a static transverse load is similar to that oc curred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with FEM predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture mechanics model developed by the second investigator and co-workers to calculate the compression after impact strength of such laminates. This approach could save significant running time when compared to FEM solutions.

Polymer-matrix composites subjected to low-velocity impact: effect of laminate configuration

Effect of laminate configuration on the impact behaviour of different polymer-matrix composites subjected to a transverse central low-velocity point impact load has been studied. For this a 3D transient finite-element analysis code using a modified Hertz law has been used. Quadratic failure criteria have been used to predict in-plane and interlaminar failure initiation. The studies have been carried out with plate dimensions of 150 mm×150 mm×6 mm with a simply supported boundary condition. For these studies, an incident impact velocity of 3 m/s and an impactor mass of 50 g have been used. Studies have been carried out on different mixed composites, cross-ply laminates, woven-fabric composites and 3D composites. It is observed that mixing of unidirectional and woven-fabric layers leads to the reduction of the failure function.

Elasto-plastic response of free–free beams subjected to impact loads

This paper presents an elasto-plastic analysis of free–free beams subjected to single point impact load and two-point impact load within the framework of finite element method. The Newmark's time integration algorithm is used to solve coupled non-linear equations of motion of the beam and the impactor. The contact force has been evaluated using elasto-plastic contact law. In the present analysis, transient response of the beam and the local response of the beam to the impactor are obtained. Numerical results indicate that the interaction between the faster reflected waves and slower progressive waves determines the final deformed configuration of the free–free beam. The speed of the plastic hinge and the effect of material strain-rate sensitivity on the impact response are discussed. It is observed that the apparent speed of moving plastic front (hinge) is not uniform throughout the impact event. The energy used for the rigid body displacement and the elastic-plastic deformation has been reported. It is observed from the present analysis that, in some cases, the gain in kinetic energy of the beam is enough to cause separation between the impactor and the beam.

Polymer Matrix Woven Fabric Composites Subjected to Low Velocity Impact: Part III—Effect of Incident Impact Velocity and Impactor Mass

The studies have been carried out on the damage initiation behavior of polymer matrix woven fabric composite plates subjected to a transverse central low velocity point impact load. Specifically, the effect of incident impact velocity and impactor mass for the same incident impact energy on the impact behavior has been investigated with a square plate of 150 mm × 150 mm × 6 mm. The material systems considered are: E-glass/epoxy and T300/5208 carbon/epoxy woven fabric composites. Inplane failure of the layers in the form of matrix cracking / lamina splitting and delaminations were the primary objectives of the study. The studies have been carried out using an in house Finite Element Analysis code. The inplane failure functions and the interlaminar failure functions have been predicted using quadratic failure criteria. It is observed that the use of incident impact energy alone as a parameter to characterize the impact behavior is inadequate. Instead, the effect of both incident impact velocity and impactor mass should be considered separately.

Polymer Matrix Woven Fabric Composites Subjected to Low Velocity Impact: Part II-Effect of Plate Thickness

The studies have been carried out on the damage initiation behavior of polymer matrix woven fabric (WF) composite plates subjected to a transverse central low velocity point impact load. Specifically, the effect of composite plate thickness on the impact behavior has been investigated with a square plate of 150 mm x 150 mm with thicknesses varying from 4.5 mm to 8.0 mm. The material systems considered are: E-glass/epoxy and T300/5208 carbon/epoxy. Inplane failure of the layers in the form of matrix cracking/lamina splitting and delaminations were the primary objectives of the study. The studies have been carried out using an inhouse Finite Element Analysis (FEA) code. The inplane failure functions and the interlaminar failure functions have been predicted using quadratic failure criteria. General observations on the impact behavior of polymer matrix WF composites as a function of plate thickness have been presented.

Polymer Matrix Woven Fabric Composites Subjected to Low Velocity Impact: Part I-Damage Initiation Studies

An investigation was undertaken to study the damage initiation behavior in polymer matrix laminated composite plates subjected to a transverse central low velocity point impact load. Inplane failure of the layers in the form of matrix cracking/lamina splitting and delaminations were the primary objectives of the study. The study has been carried out using modified Hertz contact law and an inhouse three-dimensional transient finite element analysis (FEA) code. The inplane failure functions and the interlaminar failure functions have been predicted using quadratic failure criteria. The inhouse FEA code was validated with other analytical studies and the experimental results in our earlier work. The present studies have been carried out on different plain weave fabric laminated composite plates, simply supported on all four sides. For comparison, impact behavior of balanced symmetric crossply (CP) laminates made of unidirectional (UD) layers and UD composites has been included. The studies have been carried out with plate dimensions of 150 mm x 150 mm with different plate thicknesses. Incident impact velocity in the range of 1 m/sec to 3 m/sec and impactor mass of 50 gm are considered. General observations on the distribution of failure functions and the initiation of damage are presented.

Transient response due to a pair of antiplane point impact loading on the faces of a finite griffith crack at the bimaterial interface of anisotropic solids

The transient elastodynamic problem involving the scattering of elastic waves by a Griffith crack of finite width lying at the interface of two dissimilar anisotropic half planes has been analysed. The crack faces are subjected to a pair of suddenly applied antiplane line loads situated at the middle of the cracked surface. The problem has first been reduced to one with the interface crack of finite width lying between two dissimilar isotropic elastic half planes by a transformation of relevant coordinates and parameters. Spatial and time transforms are then applied to the governing differential equations and boundary conditions which yield generalized Wiener–Hopf type equations. The integral equations arising are solved by the standard iteration technique. Physically each successive order of iteration corresponds to successive scattered or rescattered wave from one crack tip to the other. Finally, expressions for the resulting mode III stress intensity factors are determined as a function of time for both symmetric and antisymmetric loadings. Each crack tip stress intensity factor has been plotted versus time for four pairs of different types of materials.

Dynamic stress analysis of a tapered cantilever square plate under impact load

In this paper the effects of different types of variations in profile and thickness on the amplitude of vibration and the dynamic bending stresses of a square cantilever plate subjected to a point impact load have been investigated. A four-noded plate bending element was used for the analysis. In each case the results obtained for different thickness variations are compared with those obtained for the uniform thickness plate. It is observed that considerable reductions in amplitude and/or bending stresses can be achieved by proper selection of thickness variation.

Transient waves in a composite laminated plate excited by a point impact load.

Transient waves in a composite laminated plate excited by a point impact load.

Transient waves in a composite laminated plate excited by a line impact load.

A numerical method which has been presented by the authors is extended to the computation of the transient waves in a composite laminated plate excited by a point impact load. The laminated plate is divided into N plate elements, and the principle of virtual work is applied to reduce the three-dimensional equation of motion to a two-dimensional one. The method of Fourier transforms in conjunction with modal analysis is used to determine the response of displacements. Two numerical examples are computed and discussed; one is for an isotropic plate and the other is for a hybrid composite laminated plate.