V.P.W. Shim

Finite-element modeling of the ballistic impact of fabric armor

This paper investigates the finite-element simulation of ballistic impact on Twaron® fabric through proposing a material model, which incorporates viscoelasticity and a strain-rate-sensitive failure criterion. A non-linear, explicit, three-dimensional finite-element code DYNA3D is used to simulate the response of fabric under high-speed projectile impact. The fabric is modeled using membrane elements. Suitable material properties to account for its viscoelastic nature are obtained through mathematical manipulation of the three-element spring-dashpot model and by use of available experimental data. The ballistic limit, residual velocity, energy absorption and transverse deflection profiles of the fabric are predicted and compared with those from experiment. The limitations of the proposed model, in terms of representing fabric behavior such as frictional effects between yarns and unraveling and fraying of yarns are recognized. Nevertheless, the model provides a fairly accurate representation of the strain-rate-dependent behavior of fabric.

Modelling deformation and damage characteristics of woven fabric under small projectile impact

Fabrics comprising highly oriented polymers possess high impact resistance and are often used in flexible armour applications. As these materials are viscoelastic, accurate modelling of their impact and perforation response requires formulation of constitutive equations representing such behaviour. This study incorporates viscoelasticity into the formulation of a model to analyse the impact of small spherical projectiles on plain-woven PPTA poly(p-phenylene-terephthalamide) fabric. The fabric is idealized as a network of viscoelastic fibre elements and a three-element viscoelastic constitutive model is used to represent polymer behaviour. Viscoelastic parameters are used to reflect intermolecular and intramolecular bond strengths as well as the static mechanical properties of fibres. Results of the theoretical analysis were compared with data from experimental tests on fabric specimens subjected to projectile impact ranging from 140 m/s to 420 m/s. Predictions of the threshold perforation velocity and energy absorbed by the fabric showed good agreement with experimental data. The proposed analysis is able to model deformation development and rupture of the fabric at the impact point. Fraying and unravelling of yarns are also accounted for. The study shows that a knowledge of static mechanical properties alone is insufficient and results in gross underestimation of impact resistance. An important parameter identified is the crimping of yarns. Yarns in woven fabric are not initially straightened out and hence part of the stretching in fabric is due to the straightening of yarns. The effect of crimping was found to be significant for high impact velocities.

Dynamic mechanical properties of fabric armour

Abstract Twaron ® , a fabric made from aramid fibres and somewhat similar to the commonly known Kevlar ® , is also often used in flexible armour applications and hence subjected to high rates of loading. The dynamic mechanical properties of Twaron ® fabric are examined via high-speed tensile tests on specimens using a split Hopkinson bar. The load-deformation and failure characteristics at different rates of stretching are determined, from which constitutive equations representing its viscoelasticity and strain-rate dependence are formulated. This facilitates modelling of the material response to impact and perforation. Experimental results indicate that Twaron ® is highly strain-rate dependent; the tensile strength and modulus increase with strain rate while the failure strain decreases. Twaron ® specimens are also observed to fail in a more brittle fashion as the strain rate increases; this phenomenon significantly reduces the amount of energy absorbed at high strain rates. An analysis based on the morphology and fracture mechanisms of poly( p -phenylene-terephthalamide) (PPTA) fibres, the main constituent of Twaron ® , is formulated to account for the experimental observations. The proposed constitutive equation, based on a three-element linear viscoelastic model is able to describe reasonably accurately the experimental stress–strain response over a range of strain rates.

A visco-hyperelastic approach to modelling the constitutive behaviour of rubber

Abstract A visco-hyperelastic constitutive equation is proposed to describe the large-deformation response of incompressible rubber under high strain rates. The equation comprises two parts — a component with three parameters to characterise static hyperelastic behaviour, and another also with three parameters to define rate-sensitivity and strain history dependence. Relatively straightforward static and dynamic experimental techniques are employed to determine the six parameters in the constitutive relationship. Comparison of predictions based on the proposed model with experiments shows that it is able to aptly describe visco-hyperelastic behaviour of rubber-like materials under high strain rates. The material model is also used in a simulation of the three-dimensional dynamic response of a rubber pad to impact. Comparison with experimental results shows that there is good agreement with the simulation.

A review of board level solder joints for mobile applications

The reliability of electronics under drop-shock conditions has attracted significant interest in recent years due to the widespread use of mobile electronic products. This review focuses on the drop-impact reliability of lead-free solder joints that interconnect the integrated circuit (IC) component to the printed circuit board (PCB). Major topics covered are the physics of failure in drop-impact; the use of board level and component level test methods to evaluate drop performance; micro-damage mechanisms; failure models for life prediction under drop-impact; modelling and simulation techniques; and dynamic stress–strain properties of solder joint materials. Differential bending between the PCB and the IC component is the dominant failure driver for solder joints in portable electronics subjected to drop-impact. Board level drop-shock tests correlate well with board level high speed cyclic bending tests but not with component level ball impact shear tests. Fatigue is the micro-damage mechanism responsible for the failure of solder joints in the drop-shock of PCB assemblies and the fatigue strength of solder joints depends strongly on the strain rate, test temperature, and the sequence of loading. Finally, tin-rich lead-free solders exhibit significantly higher strain rate sensitivity than eutectic SnPb solder.

An Experimental Study of Low Velocity Impact Damage in Woven Fiber Composites

A study is made on the low velocity impact response and post-impact mechanical capacity of woven fiber [0/90,-45/45,0/90]s carbon epoxy composite plates. This complements the work done by numerous other researchers who have also examined low velocity impact of composites, but have focused on unidirectional, cross-ply or quasi-isotropic laminates. In the present study, post-impact static uniaxial tension, compression, as well as tension-compression fatigue tests are performed. The damage mechanisms for woven laminates are found to be predominantly delamination and fiber breakage, with the area of impact-induced delamination increasing linearly with impact energy for the range of energies examined. Damage extent and type are also dependent on the curvature of the impactor tip and deformation generated by a sharp impactor is more localized. The existence of a threshold energy level below which no delamination discernible by C-scan occurs is noted. In contrast with previous findings, it is observed that the peak in the impactor deceleration-time response is not associated with the onset of fiber failure, which can occur earlier. The amount of energy absorbed when this peak occurs therefore does not indicate the energy required to initiate fiber breakage. It is observed that residual tensile strength is a function of delamination area and impactor tip radius. For static compression and tension-compression fatigue, the residual load-bearing capacity is only dependent on delamination area. Under compression, delamination promotes the micro-buckling of fibers, whereas in tension, failure is predominantly via fiber breakage. For a common impact energy and impactor, a damaged specimen is weaker in compression than in tension.

An empirical strain rate-dependent constitutive relationship for glass-fibre reinforced epoxy and pure epoxy

Abstract An investigation into the effect of strain rate on glass-fibre reinforced plastic (GFRP) and pure epoxy subjected to compressive loading has been conducted. Experimental results in this study were obtained by a hydraulically driven Instron Testing machine and a Split-Hopkinson Pressure Bar. The range of strain rates explored was between 5 × 10 −4 s and 2500 s . A comparison between the behaviour of pure epoxy and GFRP reveals that both are strain rate sensitive, especially in the low strain rate regime. There is also a significant increase in the dynamic modulus as strain rate increases. It is shown that the stress-strain response under dynamic loading is not only a function of strain rate, but also of the strain state. An empirical equation incorporating both strain and strain rate terms is proposed and is found to adequately describe the stress-strain behaviour of both GFRP and pure epoxy for the range of loading rates studied.

Plastic deformation modes in rigid polyurethane foam under static loading

Abstract The mechanical response of rigid polyurethane foam to compression in the rise and transverse directions was examined experimentally. Compression in the rise direction yields a three-stage stress–strain response––an initial linear elastic response leading to yield, a protracted post-yield plateau and a final sharp rise in compressive stress. Other prominent features accompanying this are strain-softening and deformation localisation. Compression in the transverse direction however, gives rise to a monotonously increasing stress–strain curve and always produces uniformly distributed deformation. This difference in deformation is attributed to anisotropy in the internal cellular structure that arises from the fabrication process. To describe deformation localisation in the foam rise direction, a simple theoretical analysis employing the concept of deformation bands is proposed. This analysis involves the parameters of deformation band thickness, band front propagation velocity, strain and strain rate within the band front, and is shown to correlate well with experiments.

Mechanical response of PCBs in portable electronic products during drop impact

There is a need for more detailed studies on the drop impact reliability of electronic packages, in view of the fact that solder interconnections are becoming smaller, and portable electronic products such as mobile phones can be easily dropped during usage. This paper investigates the mechanical response of printed circuit boards (PCBs) inside portable consumer electronic products, when such products are subjected to drop impact. The response of the PCB is studied because it is one possible factor causing the failure of the interconnections with IC packages. The board response is measured via accelerations and strains at specified locations on the board. The drop test experimental results are consistent with drop orientation and physical structure of the products.

Numerical simulation of the drop impact response of a portable electronic product

The ability of portable electronic products like cellular phones and personal digital assistants to withstand accidental impacts and shock is a valuable attribute consumers expect and manufacturers desire. Usually, manufacturers conduct expensive experimental drop tests to determine the fragility of such products during the product design cycle. An alternative to conducting drop tests is to perform numerical simulation. This paper examines the feasibility of studying the drop impact response of an electronic pager using a finite element software, ABAQUS/Explicit. Experimental drop test results are then used to compare with that of numerical simulation. Parameters examined include surface strains on pager housing and impact force. Comparisons show good correlation between experimental and numerical results. Finite element computation allows critical impact orientations and drop heights to be identified so that selective experimental drop tests can be performed to determine the actual physical robustness of these products.