Search

Numerical simulations are increasingly becoming an important tool to obtain efficient designs of protective structures, and the existing literature shows that many phenomena can be accurately described by standard methods and models. This thesis, specifically, focuses on novel methods of modeling and simulating ballistic impact. Experiments are needed to validate such simulations, so numerous tests were conducted to investigate how projectile nose-shape, plate layering, target strength, ductility, and work hardening affect the penetration and perforation behavior of various structural configurations. Aluminum plates, steel plates, sand, and sand in combination with aluminum profiles were considered. These tests provide new information about the behavior of materials subjected to ballistic impact, and are valuable input for the evaluation of the numerical simulations. The novel node-splitting method, used to introduce fracture into a numerical model, and a newly implemented discrete particle method were particularly important in this work. The thesis consists of six individual parts. They are contextualized and linked together by a synopsis which includes a state-of-the-art of numerical modeling of ballistic impact and the objectives and scope of the thesis, along with summaries of the different parts, an overall conclusion and suggestions for further work. Part 1 considers low-velocity impact of layered thin steel plates. Two impactor nose shapes were used: blunt and ogival. The experimental setup is explained in detail and it was found that the resistance to perforation is highest for the blunt-nosed impactor. It was further seen that a monolithic configuration dissipates more energy than a layered configuration of the same thickness. The numerical model was able to predict the correct failure mechanisms and the trends from the experiments; however, a one-to-one relation between simulations and experiments was not obtained. In Part 2, microstructural modeling was used to determine the constitutive behavior of the base material and the heat affected zone (HAZ) of welded Al-Mg-Si aluminum alloy extrusions. Finite element simulations were conducted of impacts by 7.62 mm armor piercing bullets. The experimental validation showed that the purely numerical procedure to estimate the perforation capacity was accurate. Part 3 investigated the influence of target fragmentation on the capacity of plates subjected to ballistic impact. This was done by firing blunt and ogival-nosed projectiles at 20 mm thick plates made of four different tempers of aluminum alloy AA6070. It was shown that strength is not the only important parameter for the perforation resistance; ductility must be factored into the design as well. Node splitting, where new element faces are created at failure, was applied and evaluated in the numerical part. It was found to give as good, or better, results than conventional element erosion. In Part 4, node splitting was used to simulate ballistic impact on layered and surface-hardened steel plates. 7.62 mm armor piercing bullets struck 12 mm thick plate configurations (1x12 mm, 2x6 mm or 3x4 mm). Plate layering was found to be disadvantageous, especially for the surface-hardened plates. Numerical simulations adequately reproduced the experimental behavior. Part 5 and Part 6 looked at penetration and perforation of sand at both high and low impact velocities. A discrete particle method (DPM) where each individual sand grain is treated as a particle was used in the numerical parts of these studies. The DPM gave promising qualitative and quantitative results, and if we also consider results from other studies it becomes clear that the DPM has the potential to be used in a wide range of applications.

A purely numerical procedure for predicting the perforation resistance of welded extruded AA6082-T6 aluminum profiles is presented in this study. The numerical work was conducted completely independent of the experimental tests that were only used for validation purposes. The outline of the three-step numerical procedure is as follows: (1) the temperature development due to a specified welding process is predicted by a thermal solver, (2) based on the chemical composition of the alloy, the temperature-time history during aging and the welding analysis, the yield strength and flow stress of the material were determined; and (3) the ballistic limit velocity is found using explicit finite element simulations. The experimental validation program is described and it shows that the ballistic limit velocities found from the impact experiments correlate closely with the numerically predicted values obtained without any physical material or component tests. Further, welding of the 10 mm thick extrusions gives a 10% degradation of the capacity in terms of ballistic limit velocity compared to the unaffected material. © Owned by the authors, published by EDP Sciences, 2015. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

The thesis includes a summary of important theory in the fields of impact engineering and plasticity theory, and a literature study is carried out on aluminium designations, alloying and heat treatment. The true stress-strain curves of aluminium alloy AA6070 in O-, T4-, T6-, and T7-configurations are identified by tensile tests where the behavior is continuously measured to fracture. The aluminium was delivered as 20 mm rolled plates; microstructural images and strain ratios are reported. Material constants are found by direct calibration and inverse modeling. Ballistic tests are done in a laboratory using 7.62 mm APM2 bullets, 20 mm blunt projectiles and 20 mm ogival projectiles (CRH = 3). From these tests the ballistic limit curves and the ballistic limit velocities are found for all temper/projectile combinations. In the material tests it was shown that the O-temper is the most ductile temper and consequently almost no fragmentation takes place in the ballistic tests for this temper. The T6-temper proved to be brittle, and fragmentation was commonly seen in the ballistic tests. The degree of fragmentation is found to be of vital importance for the ballistic performance. The Cockcroft-Latham fracture criterion is implemented by using the plastic work to fracture. Numerical analyses are performed with the IMPETUS Afea Solver and LS-DYNA, with 3D-models and 2D axisymmetric models, respectively. Ballistic limit curves and the ballistic limit velocities are calculated on the basis of the numerical results and then compared to the experimental values. Limited sensitivity studies are conducted on mesh size, heat-expansion dependency, strain-rate dependency, etc. Overall the results from 2D axisymmetric models are found to be consistent with previous studies, and the 3D-analyses carried out with the IMPETUS Afea Solver gave some good results. The IMPETUS Afea Solver proved to be a user-friendly finite element program with some powerful features. In addition to the numerical studies, a thorough derivation of the Cylindrical Cavity Expansion Theory (CCET) is given. Results from CCET are good for 7.62 mm APM2 bullets. A case-study where the ballistic performance is determined without conducting any experiments is also conducted. The results are promising, but less conservative than the original simulations, due to the inability to calibrate a fracture criterion. Some suggestions for further work within the field of impact engineering and the application of the finite element method are provided at the end of the thesis, followed by an appendix that includes graphical representations and photographs of the multiple material tests and program-codes written for use in the thesis.

This thesis represents a continuation of the work carried out by Susanne Thomesen during her master's thesis in 2016. The primary objectives in this thesis were to determine the ballistic properties of the high strength steel Strenx 960 Plus exposed to both ambient and cold climate, and to investigate whether the deformation and failure modes changed during ductile-to-brittle transition as the temperature was reduced. Experimental, analytical and numerical investigations were carried out. Quasi-static tensile tests were conducted at both room temperature (RT) and -40°C. It was observed that a decrease in temperature increased the values of some certain material properties. Further, high strain rate tests were conducted in a split-Hopkinson tension bar with four different specimen geometries at RT, -40°C and -60°C. An analytical model was developed in MATLAB where the influence of strain rate, stress triaxiality and temperature on enforcing brittle failure in the material was studied. The Cockcroft-Latham (CL) fracture criterion and the Richie, Knott and Rice (RKR) model was used to predict ductile and brittle failure, respectively. Within the considered range of the three different parameters, the material exhibited brittle failure for the highest initial stress triaxialities and for the lowest temperatures. For high strain rates the material tended to weaken due to adiabatic heating, resulting in dominance of ductile failure. A short study on other types of steels was also performed in order to determined for which material properties the probability for brittle failure was highest. Here, steels with low yield stress and low work hardening had the highest tendency to exhibit brittle failure based on the assumptions made in the analytical model. A metallurgical study was performed to study the fracture surfaces of some selected material tests conducted at high strain rates. Tests conducted at RT, -40°and -60°C were examined through a scanning electron microscope. A classic dimple structure was observed for all specimen surfaces, indicating ductile failure. In order to determine the ballistic properties of the material, penetration tests were carried out using both ogival and blunt nose projectiles with a nominal mass of 197 g. The tests with the blunt nose projectiles were somewhat irregular as the projectiles were damaged during testing. Tests with ogival nose projectiles were conducted at both RT and -40°C in the sub-ordnance velocity regime, in which no effect of temperature was seen for the failure mode as the target failed by ductile hole growth at both temperature levels. Ballistic limit velocity curves showed a 5% deviation between the estimated ballistic limit velocities at RT and -40°C. A small study of the penetration tests using digital image correlation (DIC) was also performed using a point tracking technique, in which good correlation was seen by comparing with the results obtained experimentally. Lastly, a numerical study was carried out in which most of the analyses were run in Impetus Afea Solver. All models were established using 3D solid elements. Selected material tests at RT and penetration tests at both RT and -40°C with ogival nose projectiles were numerically examined. Studies of the latter proved to be strongly dependent of friction. The numerically estimated ballistic limit velocities at RT and -40°C resulted in deviations of +10% and -3.5% from the respective tests conducted experimentally, i.e both non-conservative and conservative results were obtained.

The main objective of this thesis was to determine the impact behaviour of the high strength steel Strenx-960-Plus at room and low temperatures, and to investigate if the deformation and failure mode changed from ductile to brittle during ballistic perforation as the temperature was reduced. Both experimental and numerical investigations were carried out. A substantial amount of material tests were conducted to characterize the material. Quasi-static tensile tests using three different specimen geometries were carried out at both room temperature (RT) and -40 oC, where a small effect of temperature was seen. The effect of strain rate was investigated through intermediate and high strain rate tests, using a hydro-pneumatic test machine and a Split-Hopkinson tension bar, respectively. The experimental results from the intermediate strain rate tests were irregular and therefore not used in the further work. In an attempt to determine the ductile-to-brittle transition temperature (DBTT) Charpy V-notch impact test were carried out at chosen temperatures in the interval from RT to -90 oC. A significant decrease in absorbed energy was observed, but no distinct transition temperature was found. The ballistic properties of the material were tested at selected temperatures in the range from RT to -60 oC. Target plates of the material were placed in a newly built temperature chamber, and fired at using 7.62 mm APM2 bullets. Ballistic limit velocity curves were obtained, showing only a minor effect of temperature. The deformation modes seen experimentally appeared to dependent only on the initial velocity, and not the temperature. Based on the experimental results from the material tests at RT the model constants of the modified Johnson-Cook (MJC) material model, the Cockcroft-Latham (CL) fracture criterion and the Johnson-Cook (JC) fracture criterion were calibrated. Abaqus/Explicit was used in the numerical work, combined with the SIMLab Metal Model for the material input. Numerical models of the quasi-static tension tests and the high strain rate tests were used for verification and validation of the calibrated material model and fracture criteria. Numerical analyses of the Charpy V-notch test at RT proved to be highly dependent on the fracture criterion, but gave appropriate results in general. The ballistic impact test was modelled using 2D axisymmetry. The numerical results obtained provided a conservative estimate of the ballistic limit velocity at RT, deviating approximately 8\% from the experimental value. The numerical model predicted failure by ductile hole growth independent of initial velocity, which deviated visually from the experimental tests with initial velocities above approximately 800 m/s. Lastly, a metallurgical study was performed. The grain structure of the material was examined in an optical microscope, and fracture surfaces of different specimens were examined using a scanning electron microscope. Specimens from tests at both RT and -40 oC were examined. Dimples, indicating ductile fracture, was dominating for all specimens, independent of geometry and temperature. It was in general seen little effect of temperature on the ballistic properties for this material. For most practical applications the material can be regarded as ductile for the temperatures applied in this thesis.

The discrete particle approach has previously proven to give excellent agreement between experiments and numerical analysis for blast and penetration in granular medias. The main objective in this thesis is to further investigate the accuracy of the particle-based approach for penetration in granular materials, and compare the numerical output with conducted experiments. A literature survey on penetration in granular media is also carried out to understand the main mechanisms. Ballistic limit curves and ballistic limit velocities have been identified by experiments performed at SIMLab, NTNU, on empty and sand-filled AA6005-T6 aluminium panels impacted by 7.62 mm APM2 bullets. Three different fractions of granular media have been tested, with a median grain size of 0.15 mm, 0.55 mm and 0.95 mm. The experiments showed minor differences in ballistic limit velocity between each fraction of sand, but an increase of at least 32.5 % is seen when going from empty to sand-filled panels. The non-linear explicit finite element software IMPETUS Afea Solver is employed in the numerical work in this thesis. The parameters in the particle model were calibrated through numerical simulations against gas-gun component tests. In addition, drop-tower component tests were carried out, allowing the particle-based method to be validated over multiple velocity domains. The component experiments and numerical simulations are in good agreement for impacts in the high velocity domain. In the numerical simulations for empty and sand-filled panels a standard Johnson-Cook constitutive relation is used for all structural parts, while fracture is modelled with a Johnson-Cook criterion for the aluminium panel and a Cockcroft-Latham criterion for lead tip and brass jacket. The numerical results were finally compared to experimental observations, which showed that IMPETUS Afea Solver is able to capture the main trends in the perforation process. The influence of various numerical input was also investigated in a rather comprehensive sensitivity study. This showed that the input for the aluminium panel seems reasonable compared to computational cost for the complex model applied in this thesis.

The main objective of this thesis was to investigate the ballistic properties of an isotropic AlMgSi aluminium alloy both experimentally and numerically. Uncoupled and coupled fracture models were calibrated using micromechanical unit cells and existing material data, to model ductile fracture in the alloy. Ballistic impact experiments were conducted on 30 mm thick plates at the Departement of Structural Engineering at NTNU, using the steel core of 7.62 mm APM2 bullets. The Recht-Ipson model was used to obtain the ballistic limit curve, and good correspondence was seen between the curve and the experimental results. Ductile hole growth proved to be the dominant failure mechanism for all tests, with negligible fragmentation. Simplified two-dimensional micromechanical cells were analysed for different Lode parameters and triaxialities, to calibrate the Cockcroft-Latham, Johnson-Cook and Gurson-Tvergaard-Needleman (GTN) failure models. The calibrations were done with either a von Mises yield criterion or GTN in the matrix material, resulting in lower failure strains for the latter. Numerical analyses of the ballistic impacts were conducted in both IMPETUS Afea Solver and Abaqus/Explicit. A parameter study investigating the effects of strain rate, temperature and friction, concluded that friction had the largest influence on the ballistic limit velocity. Abaqus analyses gave the overall best correspondence with the experimental data, with only minor deviations between the fracture models. These deviations were probably due to the dominating temperature erosion criterion. Larger differences were seen between the models for the IMPETUS analyses. Both IMPETUS and Abaqus were able to recreate the deformation pattern seen in the experimental tests. The use of micromechanical cells for numerical modelling of ductile fracture is considered promising.

The main objective with this thesis was to investigate experimentally and numerically the effect surface hardening has on the ballistic properties of monolithic and laminated mild steel plates. 300x300 mm^2 plates of thicknesses 12 mm, 6 mm, and 4 mm were made from a low carbon structural steel (NVE36) and combined in such a way that the total thickness always was 12 mm. Some of the plates were then surface hardened by the Kverneland Group to obtain different hardness profiles; (1) as-received, (2) very hard surface with a soft core and (3) very hard surface with a hard core.Ballistic impact tests were performed at SIMLab, NTNU, using 7.62 mm AP bullets. From these tests, the Recht-Ipson model was used to obtain ballistic limit curves for all layered/hardened configurations. The experiments showed that surface hardening had a positive effect on the ballistic resistance compared to the as-received material, while lamination did not seem to influence the results significantly. The surface hardened plates suffered from radial cracks and fragmentation during penetration, while the as-received material failed by ductile hole growth.Material properties were obtained by conducting tensile tests and microhardness measurements. The material tests revealed that the plates had not been hardened to their expected hardness profiles. This affected the comparison between a soft core and a hard core configuration. The modified Johnson-Cook constitutive relation and the Cockcroft-Latham fracture criterion were chosen to represent the material behaviour. Identification of material constants was done by direct calibration in combination with Bridgman s analysis, and by inverse modelling using LS-OPT. Numerical simulations of the impact tests were conducted in IMPETUS Afea Solver with higher order 3D volume elements. Surface hardened plates were modelled with a varying yield stress over the thickness by use of scaling factors obtained from the material tests. The numerical results were finally compared with the experimental findings. IMPETUS was able to describe the main trends from the experiment and the numerical results were conservative for all the analyses.Additionally, a numerical case study was performed with nominal hardness profiles. The study showed that nominal hard core plates performed better than nominal soft core plates, while layering did not seem to affect the result significantly.