Yielding Phenomena Appeared in Impact Tensile Test Using a Split-Hopkinson Pressure Bar Method

Fast crack propagation and arrest have been studied in steel specimens of the double cantilever beam type using three different geometries and either a fixed grip or compliant loading system. A finite-difference computer program was used to measure values of the dynamic stress-intensity factor KD. The relationship between values of KD and KS, the stress-intensity factor for a quasi-statically growing crack depended on the specimen geometry and loading system used. Stable crack arrest was easier to obtain in the specimens loaded with fixed grips. This probably resulted from the rigidity of the loading system, which produced specimen oscillations after arrest of insufficient magnitude to reinitiate crack growth. An examination of the energy associated with a moving crack suggests that kinetic energy may be reabsorbed to aid further crack propagation but is not all reabsorbed at arrest. The remaining fraction causes oscillations of the cracked specimen halves which may reinitiate the crack, or be damped out as the stress intensity rings down to its static value. Examination of the data suggests that intermediate arrests, characterized by a minimum in the crack length velocity curve, were a common feature of all tests. The stress intensity for crack arrest appeared to depend on specimen geometry.

Reinforcing cement-based materials by nanomaterials has attracted extensive attention over the past decades. It has been reported that the mechanical properties of cement-based materials can be greatly improved by incorporating a small amount of nanomaterials. However, experimental and theoretical works have all focused on the enhancement of cement-based materials subjected to static loading. To the author’s knowledge, no studies have reported on the mechanical properties of nanomaterial- reinforced cement-based composites under high strain rate loadings. This study investigates the reinforcing effect of graphene oxide (GO) on cement mortar under high strain loadings. GO is an emerging nano-scale candidate for enhancing cement-based materials, which is valued for its two-dimensional geometry, superior mechanical properties and large surface area. Tensile splitting and compression tests were conducted on GO-reinforced cement mortar under both static and high strain rate loadings. The high strain rate testing was performed using a Split Hopkinson Pressure Bar (SHPB) apparatus. Static experiments showed that incorporation of GO (of 0.02 wt% of cement) improved the tensile splitting and compression strength of plain cement mortar by 8.9% and 10.8%, respectively, and there was little difference between the 0.02 wt% and 0.04 wt% GO addition. The SHPB tests showed that the reinforcing effect of GO under high strain rate is directly related to the number of cracks. In tensile splitting tests, because the major crack is always localized in the centre of the specimen regardless of the strain rate, the reinforcing effects of GO on cement mortar were the same for different strain rates. In compression tests, however, because the cracks were diffused and there were more cracks under high strain rates, the reinforcing effect of GO was also more significant under higher strain rates. To understand the reinforcing mechanisms of the nanomaterials, the key is to determine the interaction properties between the nano-scale reinforcements and the cement matrix. However, understanding of the governing forces in the reinforcement’s pull-out behaviour at such a small scale is still very limited. The present study is the first to identify the governing force during the pull-out of atomically thin two dimensional (2D) nanosheets (e.g. graphene and its derivative GO) and to develop corresponding theoretical models. In molecular dynamic (MD) simulations, friction was found to make negligible contribution to the pull-out force because of the lack of asperities on atomically thin materials (ATM). The pull-out force was revealed to be governed by a “crack plane adhesion”. Unlike frictional pull-out, crack plane adhesion produces a pull-out force independent of the embedded length of ATM. The magnitude of pull-out force and its affecting factors were investigated by MD simulations. On the basis of crack plane adhesion, the relations between the pull-out force and the pull-out displacement for ATMs was formulated. Furthermore, a new theoretical model was developed to predict the crack bridging stress (σB) of 2D ATMs. The magnitude of maximum σB was estimated to be 3MPa for 0.2 wt% of GO in cement matrix, which was used in the finite element simulations as discussed herein. The fundamental theory and new model proposed here serve as theoretical support for understanding and development of ATM-reinforced composite materials. Finite element simulations for static and SHPB compression tests were conducted using a micromechanical model, the microplane model. First, the microplane model was examined by comparative study with the commonly used concrete damaged plasticity model. Then finite element simulation models of static and SHPB compression tests were built in ABAQUS. For simulation of the static test, by including the calculated crack bridging stress into microplane model, the experimental compressive strength of GO-reinforced cement mortar could be accurately simulated, which validated the calculation of the crack bridging stress by the proposed model in Chapter 4 and the effectiveness of the microplane model to simulate the static behaviour of GO-reinforced cement-based composites. For simulation of the SHPB test, the microplane model with a logarithmic relation between the dynamic increase factor (DIF) and the strain rate to account for the strain rate effect worked for the simulations of plain cement mortar samples. However, for simulation of the GO-reinforced mortar samples, the simulation results give a significant underestimation compared with the experimental results under higher strain rates.

Direct observation of solid deformation at all points in a material test specimen is generally not possible. This becomes important when an internal point experiences the maximum effective deformation of the entire specimen. The simple reduction of load-displacement data to material constitutive parameters, as for inelastic tensile specimen necking, is precluded. Although the mechanics of necking has received considerable attention, the complementary issue of constitutive parameter determination from inelastic specimen experimental data has not. This investigation addresses both aspects of the problem for HY-100 steel. An experimental-computational procedure is demonstrated, which generates material constitutive parameters valid at strains beyond those at the onset of necking. Neck deformation, specimen size and specimen geometry effects are used to ensure the uniqueness of the parameters in the sense that a single uniaxial continuum true-stress–true-strain curve predicts the behaviour of laboratory specimens with different geometries. The solution parameters for HY-100 steel are developed, in the context of an incremental elastic–plastic constitutive formulation, by this procedure. These results support the view that tensile specimen necking is the result of the interaction between imperfection-free specimen geometry, material behaviour and applied load for relatively unsophisticated constitutive formulations if the constitutive parameters are accurately determined. In addition, broken symmetry of specimen deformation is computationally predicted and experimentally confirmed for long, slender specimen geometries.

High strain rate in-plane shear behavior of composites

Hot tensile tests were carried out to investigate hot ductility behavior and critical temperature range (ΔT) between zero strength temperature (ZST) and zero ductility temperature (ZDT) of tool steel grades AISI L3 and O1. The test specimens solidified from melting at cooling rate of 0.5℃/s and 3℃/s to the test temperature in the range between liquidus and 900℃. The specimens were then strained to failure at strain rate of 2x10⁻³/s and 2x10⁻²/s. Quenching test was carried out in order to investigate the microstructure occurred during hot tensile test. The microstructure that appeared in quenched specimen was then identified with SEM-EDX. It was found that the critical temperature range of the steels solidified at the slow or the fast cooling rate, widened with increasing strain rate. The specimens which solidified at slow cooling rate when tensile strained to failure at low or high strain rate, had wider critical temperature range than the specimens that solidified at fast cooling rate. For steel grade AISI L3, tensile test at high and low strain rate (after solidified at the fast cooling rate) revealed the hot ductility of 35-65%RA between 900-1250℃. Whereas, the hot ductility of the samples which solidified at slow cooling rate and pulled at slow strain rate were markedly higher than those pulled at higher strain rate between 900-1200℃. Precipitation of manganese sulfide in the interdendritic region resulted in deterioration of hot ductility of steel grade AISI L3. For steel grade AISI O1, tensile tests of specimens solidified between 900-1100℃ at slow cooling rate and low strain rate yielded higher hot ductility than those specimens pulled at high strain rate. The hot ductility of samples at fast cooling rate and low strain rate showed no difference to those samples of hot tested at high strain rate. Nevertheless, slow cooling rate affected hot ductility more than fast cooling rate for tensile tests at both high and low strain rate. Carbide precipitates of vanadium, tungsten and chromium along austenite grain boundaries influenced the ductility loss of steel grade AISI O1.

Coupled thermo-mechanical phase field modeling for shear ductile fracture at high strain rate and temperature

The strain rate-dependent behavior of a unidirectional non-crimp fabric (UD-NCF) carbon fiber/snap-cure epoxy composite loaded along the transverse direction under quasi-static and dynamic conditions was characterized. Transverse tension and compression tests at quasi-static and intermediate strain rates were performed using hydraulic testing machines, while a split Hopkinson pressure bar (SHPB) apparatus was used for transverse compression tests at high strain rates. A pulse shaper was used on the SHPB apparatus to ensure dynamic equilibrium was achieved and that the test specimens deformed homogenously with a nearly constant strain rate. The transverse tensile strength at a strain rate of 16 s−1 increased by 16% when compared to that at quasi-static strain rates, while distinct localized fracture surface morphology was observed for specimens tested at different strain rates. The transverse compressive yield stress and strength at a strain rate of 325 s−1 increased by 94% and 96%, respectively, when compared to those at quasi-static strain rates. The initial fracture plane orientation for the transverse compression tests was captured with high-speed cameras and found to increase with increasing strain rate. The study provides an important data set for the strain rate-dependent response of a UD-NCF composite material, while the qualitative fracture surface observations provide a deeper understanding of the failure characteristics.

This work deals with engineering components made of stainless steels working at high temperature and subjected to creep-fatigue loading history. The defect assessment procedures generally use the crack growth properties curve d a/d t versus C ∗ parameter for estimating the creep-crack growth. The ASTM E 1457-98 [ASTM E 1457-98. Standard test method for measurement of creep crack growth rates in metals, 1998] procedure proposes the rule to establish such a master curve. In particular, it is stipulated that this rule only applies for CT specimens. Previously [Laiarinandrasana L, Kabiri R, Drubay B. In: Gupta A, editor. Proceedings of the 16th international conference on structural mechanics in reactor technology, Washington, USA, 2001], some practical methodology to produce this crack growth curve on CT specimens has been described by introducing the way to determine the upper and lower limits of relevant experimental points and by adopting the ASTM E 1457-98 method to estimate the creep component of the load line displacement rate (d δ/d t behavior). This latter is the interesting part of the total displacement rate recorded during the test. This paper focuses on the application of the procedure proposed in [Laiarinandrasana L, Kabiri R, Drubay B. In: Gupta A, editor. Proceedings of the 16th international conference on structural mechanics in reactor technology, Washington, USA, 2001] on specimen geometries other than CT, such as circumferentially cracked round bar (CCRB) and double edged notched in tension (DENT) specimens. The d a/d t versus C ∗ curves issued from all of these specimens are compared. Discussion about the effect of geometry on these curves is carried out. Additionally, some finite element analyses have been performed in order to simulate the creep crack growth using the node release technique. These simulations allow to verify the validity of the proposed expressions of C ∗ and consequently the master curve of the 316L(N) stainless steel.

The effect of specimen geometry on the mechanical behaviour of wet porcine trabecular bone specimens was studied by destructive uniaxial compression using cylindrical and cuboid specimens with different aspect ratios (1:1, 2:1 and 3:1) but keeping the cross sectional area constant. The coefficients of determination in the resulting modulus-density and strength-density regressions (p<0.05) and the standard error of regressions were compared between the specimens. Comparing cylinder specimens, coefficients of determination for both modulus-density and strength-density regressions were highest and standard error of regressions were lowest for the 2:1 cylinders (R2 = 0.50, S.E=76MPa, modulus; R2 = 0.66, S.E=1.63MPa, strength). Comparing cuboid specimens, coefficients of determination for both modulus-density and strength-density regressions were highest for the cubes (R2 = 0.46, modulus; R2 = 0.36, strength). Comparison between 2:1 cylinders and cubes, there was no significant difference in their coefficient of determination for both modulus-density regression (p>0.05) and strength-density regression (p>0.05). However 2:1 cylinders is still a more preferred geometry for compressive testing as it achieved a moderate correlation (0.50 R² < 0.75) for both modulus-density regression and strength-density regression compared to cube which showed a weak relationship (R2<0.5) for both modulus-density regression and strength-density regression.

The effect of the specimen geometry on the measured fatigue life was investigated in this study. Low-cycle fatigue tests with hollow and solid specimens were performed and the differences in the two different specimen geometries were observed. A difference in the fatigue life between the hollow and solid specimens exists when the strain is large and diminishes as the strain decreases, which indicates that the difference stems from the crack propagation stage rather than the crack initiation stage. Two-dimensional finite element analysis was performed to quantify the effects of the specimen geometry in terms of the stress and strain near the crack tip. Larger internal plastic strain in the hollow specimen was found. This led to a higher plastic strain energy density and could explain the difference in the lifespan using the two specimen geometries.

Ti-6Al-4V alloy is one of the most important engineering alloys, combining attractive properties with inherent workability. The aim of this study is to investigate the effect of strain rate on the compressive mechanical properties of Ti6Al4V alloy manufactured by a selective laser melting process. The mechanical tests were performed by means of a compression split Hopkinson pressure bar apparatus under high strain rate ranging from 1400 s-1 to 4500 s-1. The true stress-strain curves obtained from static and dynamic compressive tests show strain rate sensitivity from quasi-static (peak strength 1300MPa) to high strain rate (peak 1500 MPa). Within the high strain rate range tested, the strain rate sensitivity is not remarkable. The fractographic analysis shows a relatively smooth and smeared fractured surface along with a dimple like structure. The observation of elongated dimples confirms the operation of a dynamic shear failure mechanism for the additively manufactured Ti-6Al-4V parts.

Knowledge of the properties of soft, viscoelastic materials at high strain rates are important in furthering our understanding of their role during blast or impact events. Testing these low impedance materials using a metallic split Hopkinson pressure bar setup results in poor signal to noise ratios due to impedance mismatching. These difficulties are overcome by using polymeric Hopkinson bars. Conventional Hopkinson bar analysis cannot be used on the polymeric bars due to the viscoelastic nature of the bar material. Implementing polymeric Hopkinson bars requires characterization of the viscoelastic properties of the material used. In this paper, 30 mm diameter Polymethyl Methacrylate bars are used as Hopkinson pressure bars. This testing technique is applied to polymeric foam called Divinycell H80 and H200. Although there is a large body of of literature containing compressive data, this rarely deals with strain rates above 250s−1 which becomes increasingly important when looking at the design of composite structures where energy absorption during impact events is high on the list of priorities. Testing of polymeric foams at high strain rates allows for the development of better constitutive models.

Design and Development of an Integrated Compressive - Tensile Polymeric Split Hopkinson Pressure Bar Setup

Two-body wear rate of PEEK, CAD/CAM resin composite and PMMA: Effect of specimen geometries, antagonist materials and test set-up configuration

In order to study the characteristics of static strength of ceramics, 3-point bending tests with a constant loading rate were carried out at room temperature in air, by using sintered silicon nitride, partially stabilized zirconia and two kinds of alumina. The effects of specimen geometry and temperature on the strength were also investigated by conducting ring compression tests for the silicon nitride at room temperature and 1300°C in air.In the 3-point bending tests, better fitness for the two-parameter Weibull distribution was found when the data were correlated with the true fracture stress evaluated at the fracture point of specimen, rather than the maximum nominal stress. The effect of specimen geometry on the strength was small for the case investigated in this study. The mean strength and the coefficient of variation of the strength at 1300°C were reduced to about half and one-third of those at room temperature, respectively.The fracture surface of the tested specimens was observed through a scanning electron microscope, and the predominant flaws were identified which were preexisting in the specimens. The equivalent crack length was evaluated taking account of the crack geometry and the stress state associated with the crack location. The fracture stress was correlated with the equivalent crack length. The results showed that the strength decreased with decreasing flaw size, compared with the estimate expected from the linear fracture mechanics concept. The tendency in the relation was explained by the modification that a material constant should be added to the original equivalent crack length.The fractographic observation suggested that the fracture of the silicon nitride at elevated temperatures followed the formation of semi-circular damage-region due to the slow crack growth. Another fracture mechanics approach was required in the analysis of the fracture of ceramics with inelastic behavior at elevated temperature.