The damage resistance of quasi-isotropic carbon/epoxy composite tape laminates impacted by high velocity ice

Transverse impact from hail ice can create internal damage to composite structures that is not visually detectable and is therefore a damage tolerance concern. This paper focuses on the experimental characterization of the damage resistance of laminates made from T800/3900-2 carbon/epoxy tape material to impact by high velocity ice spheres, i.e., simulated hail ice (SHI). The failure threshold energy (FTE) defining the onset of damage was found for three panel thicknesses (1.59, 3.11, and 4.66 mm), each impacted by three ice diameters (38.1, 50.8, and 61.0 mm). Non-destructive investigation techniques were used to detect, map, and characterize the delaminated area. A regression analysis was used to quantitatively determine the FTE of the tape laminates, which was found to closely match previous woven carbon/epoxy FTE data. Both data sets were found to exhibit a linear and common relationship to the ratio of panel thickness to ice diameter (H/D). The resulting delamination patterns of the current and previous panels were found to be similar at damage initiation, but to differ for higher damage states.     

A simple model for debris clouds produced by hypervelocity particle impact

A simple debris cloud model is developed by considering the one dimensional shock wave motion in the material together with the catastrophic fragmentation theory by Grady. The model provides a simple method for calculating the velocities at the outer perimeter of the cloud and the average particle size in the cloud.     

An analytical model for tumbling projectile perforation of thin aluminum plates

An analytical model for the perforation of thin aluminum targets by tumbling cylindrical projectiles was developed. The target material was considered to be rigid—perfectly plastic without strain hardening, while the projectile was treated as undeformable. The perforation process was experimentally found to consist of three stages: plugging, hole enlargement, and front petaling. Both conservation of energy and conservation of momentum laws were used for modeling the plugging stage, while a lower bound method was employed during the hole enlargement stage. The energy dissipated during the petaling stage consists of shearing fracture of the petal, localized plastic shear in a zone contiguous with the edges, the momentum of the petal and the bending energy of the petal. The analytical results provided generally good agreement with the corresponding experimental data in terms of the final velocity and final oblique angle of the projectile as well as the crater length of the target.     

An engineering model for deformation of CFRP plates during penetration

The response of brittle CFRP laminated plates to penetration by cylindrical indenters has been studied using a combined experimental and analytical investigation. The two major damage modes caused by delamination and plugging are found to divide the plate response into three distinct stages. An analytical model, which accounts for the geometric parameters of the response, is developed to describe the deformation behaviour of the laminate in the post-delamination stage. Using the experimental measurements of strains and displacements at the centre, the model is used to estimate the size of the internal damage (delamination) and its effective bending modulus. The predicted delamination sizes for various laminate thicknesses are successfully correlated with those measured using C-scans. The agreement instills confidence in using the present analytical approach to reduce the number of tests required to characterize the penetration response of laminates.     

An analytical model for high velocity impact on confined explosive configurations

The impact of a projectile travelling at high velocity upon confined or unconfined explosive can result in catastrophic events if detonation occurs. One important mechanism for initiation is shock. While hydrocodes with suitable burn models undoubtedly offer the best approach for the investigation of such shock induced events in detail, there is also no doubt that analytical models can be very useful in scoping studies or in the development of empirical models useful for rapid investigations under specific circumstances. With these aims in mind, a model for impact upon a confined explosive is derived using very simple models for mechanical and reactive material response. It is demonstrated by comparison with experiments that the model is effective in capturing the dependence of the critical impact velocity for detonation upon projectile diameter.     

A Weibull stress model to predict cleavage fracture in plates containing surface cracks

This study applies recent advances in probabilistic modelling of cleavage fracture to predict the measured fracture behaviour of surface crack plates fabricated from an A515-70 pressure vessel steel. Modifications of the conventional, two-parameter Weibull stress model introduce a non-zero, threshold parameter (σ_w-min ). The introduction of σ_w-min brings numerical predictions of scatter in toughness data into better agreement with experimental measurements, and calibration of this new parameter requires no additional experimental data. The Weibull modulus ( m ) and scaling parameter (σu ) are calibrated using a new strategy based on the toughness transferability model, which eliminates the non-uniqueness that arises in calibrations using only small-scale yielding toughness data. Here, the Weibull stress model is calibrated using toughness data from deep-notch C(T) and shallow-notch SE(B) specimens, and is then applied to predict the measured response of surface crack plates loaded in different combinations of tension and bending. The model predictions accurately capture the measured distributions of fracture toughness values.     

A continuous damage fracture model to predict formability of sheet metal

A continuous damage fracture model, which consists of a fracture criterion and a continuum damage constitutive law was proposed in this paper to calculate formability of sheet metal. In this model, an extension of the McClintock void growth model was selected as the fracture criterion to be incorporated with a coupled damage‐plasticity Gurson‐type constitutive law. Also, by introducing a Lode angle dependent parameter to define the loading asymmetry condition, the shear effect was phenomenologically taken into account. The proposed fracture model was implemented in user defined material subroutines in ABAQUS. The model was calibrated and correlated by the uniaxial tension, shear and notched specimens tests. Application of the fracture criterion for the Limit dome height tests was discussed and the simulation results were compared with the experimental data.     

An engineering fragmentation model for the impact of spherical projectiles on thin metallic plates

In this paper, an engineering fragmentation model is presented for the case of hypervelocity impact of a spherical projectile on a thin bumper plate at normal incidence. The range of impact velocities covered is the solid fragmentation regime up to the limits of complete melting of projectile and target material. The model was developed for an axisymmetric fragment cloud by consideration of the conservation laws for mass, momentum, and energy, as well as making a few assumptions on the morphology of the cloud. The fragment cloud is modeled discretely, i.e. each particle of the fragment cloud is considered separately in the analytical calculation. The model consists of mainly analytical relationships and a few empirical fit functions, where no analytical formulation was available. The model distinguishes between fragments originating from the projectile and fragments originating from the bumper plate. The projectile fragments are split into the central fragment and spall fragments. An exponential distribution function is assumed for the mass distribution of the projectile's spall fragments. The fragments from the bumper are assumed to have a uniform mass. All fragments are assumed to be of spherical shape. The fragmentation model was applied and calibrated during experiments, in which Al spheres impact on thin Al plates. The calibration experiments, performed using a two-stage light gas gun, were in the range of impact velocities between 4.8 and 6.7 km/s. In this velocity range, the model was calibrated against residual velocities measured and fragment mass distribution, which was indirectly determined by measuring the crater depth distributions in rear walls.     

刚性钝头弹体正贯穿中厚金属靶的挤凿块速度模型

从挤凿破坏机理出发,考虑了能量守恒定律和剪切冲塞模型,提出了适用于刚性钝头弹体(平头、半球形头、球形)正贯穿中厚金属靶的挤凿块速度模型.设计了穿甲实验,以直径8 mm钨球正冲击3 mm厚GH4169靶板,得到了球形弹体相应的挤凿块数据,结合文献中平头和半球形头弹体实验数据验证了挤凿块速度模型的适用性,模型计算结果与实验...     

Analytical and numerical investigation of polyurea layered aluminium plates subjected to high velocity projectile impact

This paper discusses on the penetration of high velocity projectiles through aluminium–polyurea composite layered plate systems. An analytical model has been proposed to predict the residual velocity of aluminium–polyurea composite plates, and validated with both experimental and numerical investigations. Full metal jacket (FMJ) projectiles (5.56 mm × 45 mm), corresponding to NATO standard SS109, were fired at the aluminium–polyurea composite layered plate systems from a distance of 10.0 m at a fixed velocity of 945 m/s. Four different composite plate configurations were used with thicknesses varying from 16 to 34 mm. Each configuration consisted of six specimens. Residual velocities for each individual test were recorded. Numerical simulations of the penetration process have been performed using advanced finite element code LS-DYNA®. The well-established Johnson–Cook and Mooney–Rivlin material models were used to represent the stress–strain behaviour of aluminium and polyurea in the numerical analysis. The analytical and numerical models provided good approximations for the residual velocities measured during the experimental tests. Polyurea layers contributed positively towards the reduction of residual velocity of the projectile in composite plate systems. In addition, ballistic limit curves for different composite systems have been established based on the validated models. As the results showed that polyurea contributes positively towards the reduction of residual velocity of projectiles, the findings of this study can be effectively used for the similar applications in future armour industry.     

Experimental study on expansion characteristics of debris clouds produced by oblique hypervelocity impact of LY12 aluminum projectiles with thin LY12 aluminum plates

Tests of hypervelocity projectile impacts to a double-wall structure made of LY12 aluminum were performed using a two-stage light gas gun. In the bumper plate hole analysis, empirical equations that relate hole dimensions to impact parameters such as velocity, angle of obliquity and bumper plate thickness are obtained. The laser shadowgraphs in order to get the expansion of debris clouds were taken and the characteristic parameters obtained. The damage effects of the back wall varying with impact parameters were studied. The expansion of debris clouds was determined.     

An approach to evaluate the impact damage initiation and propagation in composite plates

An approach to evaluate the impact damage initiation and propagation in composite plates is investigated. It is shown that the main characters of impact damage can be predicted by introducing both threshold strength and propagation strength for matrix cracking. The threshold strength controls whether the damage occurs in the composite structures, whereas the propagation strength determines by which extent the damage develops. Maximum stress and quadratic stress failure criteria were employed in three failure modes. It has been revealed from both the simulation and the experiment that there is a small zone of no matrix failure at the centre of impact area in the core for 0.59 J impact. It is shown that this approach has flexible applications at an appropriate stage in the design and research process.     

An analytical model to predict impact behaviour of soft armours

This paper presents a newly developed analytical model for predicting the impact behaviour of soft armours. It can be used to calculate the armour ballistic curve as well as the impact force, the tension in each layer, the displacement and velocity of the layers and projectile, the yarn stresses and strains and the damaged area. Fibres are assumed to be linear elastic up to fracture and the projectile perfectly rigid.     

Influence of surface coating on ballistic performance of aluminum plates subjected to high velocity impact loads

Ballistic response of single or multi-layered metal armor systems subjected to high velocity impact loads was investigated in many experimental, theoretical and numerical studies. In this study, influences of plasma spray surface coating on high velocity impact resistance of AA 6061 T651 aluminum plates were analyzed experimentally. Two different types of surface coating were applied to plates using plasma spray. Using 9.00 mm Parabellum bullets, ballistic performance of both uncoated and coated plates was tested. After the impact tests, penetration depth including plate bending on the front face and bulging on the rear face of the target plate was measured. The improvement on the ballistic resistance of the coated plates was clearly observed. The increase in non-perforating projectile velocity and the decrease in penetration depth were both experienced.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Finite element analysis to predict penetration and perforation of thick FRP laminates struck by projectiles

This paper examines the penetration and perforation of fibre-reinforced plastic (FRP) laminates struck by rigid projectiles with different nose shapes within a wide range of impact conditions using ABAQUS/Explicit code. It is assumed that the FRP laminate target response can be represented by a velocity dependent forcing function which eliminates discretizing the target as well as the need for a complex contact algorithm. The forcing function is then applied to the surface of the projectiles as boundary conditions in the numerical model. With this combined analytical and computational technique we can obtain the depth of penetration, residual velocity, ballistic limit, transient response in terms of time-histories of displacement/penetration, velocity and deceleration of the projectile. It is shown that the model predictions are in good correlation with available experimental data.     

复合材料层合板单钉双剪连接挤压强度的一种工程估算方法

将上限理论应用到复合材料层合板单钉双剪连接挤压强度分析中, 把连接结构的位移场划分为动态区域(层合板)和静态区域(紧固件), 并认为失效发生在位移可动场和不动场之间的钉孔边受挤压部分。由于受挤压孔孔边各层应力状态不一样, 受挤压孔边各层的失效区域和失效模式也各不相同。从宏观上研究复合材料层合板单钉连接孔边的失效区域和失效模式, 结合上限理论提出了一种估算复合材料单钉连接挤压强度的工程算法。通过与试验结果对比, 发现该方法能较好地预测出复合材料单钉双剪连接挤压强度。     

An integrated machine-process-controller model to predict milling surface topography considering vibration suppression

Surface topography is an important factor in evaluating the surface integrity and service performance of milling parts. The dynamic characteristics of the manufacturing system and machining process parameters significantly influence the machining precision and surface quality of the parts, and the vibration control method is applied in high-precision milling to improve the machine quality. In this study, a novel surface topography model based on the dynamic characteristics of the process system, properties of the cutting process, and active vibration control system is theoretically developed and experimentally verified. The dynamic characteristics of the process system consist of the vibration of the machine tool and piezoelectric ceramic clamping system. The dynamic path trajectory influenced by the processing parameters and workpiece-tool parameters belongs to the property of the cutting process, while different algorithms of active vibration control are considered as controller factors. The milling surface topography can be predicted by considering all these factors. A series of experiments were conducted to verify the effectiveness and accuracy of the prediction model, and the results showed a good correlation between the theoretical analysis and the actual milled surfaces.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-021-00386-7     

A modification to the mathematical model of perforation by Dikshit and Sundararajan

In this paper a modification is made to the theory of perforation given by Dikshit and Sundararajan (Int. J. Impact Engng. 12(3) (1992) 373–408). In their analyses an empirical equation is used to compute the normalized size of the plastic zone around the projectile path in the target material. In this paper by assuming that the heat generated in the perforation process effects only in the plastic zone, an analytical equation is introduced instead of an empirical relationship for computation of the normalized size of the plastic zone. The final results of this paper are in good agreement with those of Dikshit and Sundararajan.