High Strain Rate Sensitivity Research Articles

Diffusion Bonding of Austenitic Stainless Steel 316L to a Magnesium Alloy

Dissimilar metal combinations are often necessary when manufacturing a component in order to meet particular functional and engineering requirements or protect against environmental degradation. Stainless steels are used in a diverse range of applications due to their excellent corrosion resistance, formability and strength. The 316L stainless steel also shows good crashworthiness due to its high strain rate sensitivity which makes it suitable for the transportation industry. The joining together of the 316L steel and AZ31 magnesium alloy cannot be achieved using conventional fusion welding methods and therefore, diffusion bonding using interlayers was used to overcome the differences in their physical properties. The results show that Cu and Ni interlayers form a eutectic with the magnesium which enhances wettability and bond formation through isothermal solidification. The effect of hold time on the microstructural developments across the joint region was studied at a bonding temperature of 530oC and 510oC for the Cu and Ni interlayers respectively using a bonding pressure of 0.2 MPa. This preliminary investigation shows that by increasing the bonding time from 5 to 60 minutes results in a Cu-Mg and Ni-Mg eutectic phase structure forming along the bond interface. By holding the joint at the bonding temperature for 15 minutes initiates isothermal solidification of the joint and this was confirmed by DSC analysis. However, the movement of the solid/liquid interface on solidification pushes intermetallic phases into the center of the bond during the solidification stage. The intermetallics increase the hardness value of the bond interface and lower final bond strengths.

Evaluation of Charpy Impact Test Performance for Advanced High-Strength Steel Sheets Based on a Damage Model

The Charpy impact test performance was experimentally and numerically studied for two advanced high-strength steel sheets (AHSS) TWIP940 and TRIP590 as well as for a high strength grade 340R. Uni-axial simple tension tests were performed to determine their anisotropic properties and strain rate sensitivities along with their hardening behaviour. The high speed strain rate sensitivity of TRIP590 and 340R (rate sensitive) was also characterized to account for high strain rates involved in the Charpy impact test. To evaluate fracture behaviour in the Charpy impact test, a new damage model, including the triaxiality-dependent fracture criterion and the hardening behaviour with stiffness deterioration, was introduced and the model was calibrated based on the simple tension and V-notch tests. The new damage model along with the anisotropic yield function Hill1948 was incorporated into the ABAQUS/Explicit FEM code, which performed reasonably well to predict the impact energy absorbed during the Charpy impact test.

Deformation behavior of an ultrafine grained two phase Co–Cu alloy processed by electrodeposition

An ultrafine grained two phase Co–Cu alloy was processed by electrodeposition. The two phase Co–Cu alloy was composed of hexagonal close-packed Co-rich grains and face-centered cubic Cu-rich grains. The two phase Co–Cu alloy exhibited a high strain rate sensitivity of 0.137 and low activation volume of 3.3 b Co 3 or 3.1 b Cu 3 at room temperature. It is suggested, from the results of an atomic simulation of the Co/Cu grain boundary, that the unique deformation characteristics can be attributed to Co/Cu heterogeneous grain boundaries.

Enhanced ductility of high-strength electrodeposited nanocrystalline Ni–Co alloy with fine grain size

A nanocrystalline (nc) Ni–49.2 mass% Co alloy with an average grain size of 15 nm was synthesized by electrodeposition. Uniaxial tensile tests performed at room temperature and different strain rate showed that the nc Ni–Co alloy exhibits high strength of 1920–2250 MPa and enhanced ductility of 10–13%. The grain refinement, solid-solution hardening and decrease of stacking fault energy, which are caused by alloying of Co element, should be responsible for the excellent mechanical performance. It was deduced from the high strain-rate sensitivity and apparent activation volume that dislocation activity is the dominant deformation mechanism although grain boundary activity may be expected in this alloy.

Failure mechanism of Pb-bearing and Pb-free solder joints under high-speed shear loading

The failure behaviors of ball grid array (BGA) solder ball joints under the various loading speeds of the high-speed shear test were investigated both experimentally and with non-linear, 3-dimensional finite element modeling. Conventional Sn-37Pb and Pb-free, Sn-3.5Ag solder alloys were used to compare the failure behaviors. Far greater shear forces were measured by the high-speed shear test than by the low-speed shear test. The shear force further increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloys. Brittle interfacial fractures were more easily achieved by the high-speed shear test in the Sn-3.5Ag solder joints, especially at higher shear speed. This result was discussed in terms of the relationship between the strain-rate of the solder alloy, the work-hardening effect, and the resulting stress concentration in the interfacial regions. However, no transition of the failure mode was observed in the high-speed shear test of the Sn-37Pb solder joints.

Energy consumption in rock fragmentation at intermediate strain rate

In order to determine the relationship among energy consumption of rock and its fragmentation, dynamic strength and strain rate, granite, sandstone and limestone specimens were chosen and tested on large-diameter split Hopkinson pressure bar (SHPB) equipment with half-sine waveform loading at the strain rates ranging from 40 to 150s^(-1). With recorded signals, the energy consumption, strain rate and dynamic strength were analyzed. And the fragmentation behaviors of specimens were investigated. The experimental results show that the energy consumption density of rock increases linearly with the total incident energy. The energy consumption density is of an exponent relationship with the average size of rock fragments. The higher the energy consumption density, the more serious the fragmentation, and the better the gradation of fragments. The energy consumption density takes a good logarithm relationship with the dynamic strength of rock. The dynamic strength of rock increases with the increase of strain rate, indicating higher strain rate sensitivity.

Nanoindentation of Advanced Polymers Under Non-Ambient Conditions: Creep Modelling and Tan Delta

The creep modelling approach described in this paper reveals a correlation between the strain rate sensitivity parameter determined from room temperature nanoindentation data and tan delta determined from conventional dynamic mechanical analysis (DMA). With recent advances in nanomechanical instrumentation it is possible to obtain reliable raw data under non-ambient conditions. Nanoindentation tests on polymeric films at elevated temperature provide support for the correlation, with high values of the high strain rate sensitivity parameter only observed in the vicinity of the glass transition temperature. Analysis of the shapes of the indentation loading curves at elevated temperature has revealed a sharp decrease in the loading curve exponent near the glass transition. The nanoindentation approach holds promise for assessment of actual components (e.g., micro-moulded components) where production of DMA test pieces is not feasible.

Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, GB zone, and grain-boundary sliding

In this paper, we formulated an atomically-equivalent continuum model to study the viscoplastic behavior of nanocrystalline materials with special reference to the low end of grain size that is typically examined by molecular dynamic (MD) simulations. Based on the morphology disclosed in MD simulations, a two-phase composite model is construed, in which three distinct inelastic deformation mechanisms disclosed from MD simulations are incorporated to build a general micromechanics-based homogenization scheme. These three mechanisms include the dislocation-related plastic flow inside the grain interior, the uncorrelated atomic motions inside the grain-boundary region (the GB zone), and the grain-boundary sliding at the interface between the grain and GB zone. The viscoplastic behavior of the grain interior is modeled by a grain-size dependent unified constitutive equation whereas the GB zone is modeled by a size-independent unified law. The GB sliding at the interface is represented by the Newtonian flow. The development of the rate-dependent, work-hardening homogenization scheme is based on a unified approach starting from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity through replacement of the Maxwell viscosity of the constituent phases by their respective secant viscosity. The developed theory is then applied to examine the grain size- and strain rate-dependent behavior of nanocrystalline Cu over a wide range of grain size. Within the grain-size range from 5.21 to 3.28 nm, and the strain rate range from 2.5 × 10 8 to 1.0 × 10 9/s, the calculated results show significant grain-size softening as well as strain-rate hardening that are in quantitative accord with MD simulations [Schiotz, J., Vegge, T., Di Tolla, F.D., Jacobsen, K.W., 1999. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971–11983]. We have also applied the theory to investigate the flow stress, strain-rate sensitivity, and activation volume over the wider grain size range from 40 nm to as low as 2 nm under these high strain rate loading, and found that the flow stress initially displays a positive slope and then a negative one in the Hall–Petch plot, that the strain-rate sensitivity first increases and then decreases, and that the activation volume first decreases and then increases. This suggests that the maximum strain rate sensitivity and the lowest activation volume do not occur at the smallest grain size but, like the maximum yield strength (or hardness), they occur at a finite grain size. These calculated results also confirm the theoretical prediction of Rodriguez and Armstrong [Rodriguez, P., Armstrong, R.W., 2006. Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals. Bull. Mater. Sci. 29, 717–720] on the basis of grain boundary weakening and the report of Trelewicz and Schuh [Trelewicz, J.R., Schuh, C.A., 2007. The Hall–Petch breakdown in nanocrystalline metals: a crossover to glass-like deformation. Acta Mater. 55, 5948–5958] on the basis of hardness tests. In general the higher yield strength, higher strain rate sensitivity, and lower activation volume on the positive side of the Hall–Petch plot are associated with the improved yield strength of the grain interior, but the opposite trends displayed on the negative side of the plot are associated with the characteristics of the GB zone which is close to the amorphous state.

Nucleation of partial dislocations at a crack and its implication on deformation mechanisms of nanostructured metals

Nucleation of partial dislocations at a crack is analyzed based a multiscale model that incorporates atomic information into continuum-mechanics approach. The crack and the slip plane as the extension of the crack are modeled as a surface of displacement discontinuities embedded in an elastic medium. The atomic potential between the adjacent atomic layers along the slip plane is assumed to be the generalized stacking fault energy, which is obtained based on atomic calculations. The relative displacements along the slip plane, corresponding to the configurations of partial dislocations and stacking faults, are solved through the variational boundary integral method. The energetics of partial dislocation nucleation at the crack in FCC metals Al and Cu are comparatively studied for their distinctive difference in the intrinsic stacking fault energy. Compared with nucleation of perfect dislocations in previous studies, several new features have emerged. Among them, the critical stress and activation energy for nucleation of partial dislocations are markedly lowered. Depending on the value of stacking fault energy and crack configuration, the saddle-point configurations of partial dislocations can be vastly different in terms of the nucleation sequence and the size of the stacking fault. These findings have significant implication for identifying the fundamental dislocation and grain-boundary-mediated deformation mechanisms, which may account for the limiting strength and the high strain rate sensitivity of nanostructured metals.

FAILURE BEHAVIORS OF FLIP CHIP SOLDER JOINTS UNDER VARIOUS LOADING CONDITIONS OF HIGH-SPEED SHEAR TEST

The failure behaviors of flip chip solder joints under various loading conditions of the high-speed shear test (H-SST) were investigated with an experimental and non-linear 3-dimensional finite element modeling study. The solder composition used in this study was Sn -3.0 Ag -0.5 Cu ( in wt .%). The shear forces were far greater by H-SST than by low-speed shear test (L-SST). The shear force further increased with increasing shear speed, mainly due to the high strain-rate sensitivity of the solder alloy. Brittle interfacial fractures were more easily achieved by H-SST, especially at the higher shear speed. This was discussed in terms of the relationship between the strain-rate and work-hardening effect and the resulting stress concentration at the interfacial regions

Deformation behavior of an ultrafine-grained Al–Ni–Y–Co–Sc alloy

The low ductility of ultrafine-grained Al–Ni–Y–Co–Sc alloy in as-extruded condition was improved by introducing an additional processing step of warm forging at 673 K, 10 −1 s −1. The forging resulted in uniform distribution of the intermetallic particles and change in morphologies as well as a high strain rate sensitivity index ( m ∼0.02) as against 0.003 for as-extruded condition. The localized neck in tensile test in the form of a band has been attributed to Hill's criterion of plane strain ‘no deformation’ band. The other interesting observation of monotonic softening of the alloy in RT compression test has been attributed to the accumulation of damages; e.g., micro-voids/cracks, and the like.

Mechanical properties of ultrafine grained ferritic steel sheets fabricated by rolling and annealing of duplex microstructure

A new route to fabricate ultrafine grained (UFG) ferritic steel sheets without severe plastic deformation is proposed in this article. A low-carbon steel sheet with a duplex microstructure composed of ferrite and martensite was cold-rolled to a reduction of 91% in thickness, and then annealed at 620–700 °C. The microstructure obtained through the process with annealing temperatures below 700 °C was the UFG ferrite including fine cementite particles homogenously dispersed. The grain size of ferrite matrix changed from 0.49 to 1.0 μm depending on the annealing temperature. Dynamic tensile properties of the produced UFG steels were investigated. The obtained UFG ferrite–cementite steels without martensite phase showed high strain rate sensitivity in flow stress. The UFG ferritic steels are expected to have high potential to absorb crash energy when applied to automobile body.

Effect of high-speed loading conditions on the fracture mode of the BGA solder joint

High-speed ball shear test was investigated in terms of the effects of two test parameters, shear speed and shear height, with an experimental and computational simulation utilizing 3-dimensional non-linear finite element modeling for evaluating the solder joint integrity of ball grid array (BGA) packages. A representative Pb-free solder alloy, Sn–0.7Cu, was employed in this study. Far greater shear forces were measured by high-speed shear test than by low-speed shear test. The shear force further increased with shear speed mainly due to the high strain-rate sensitivity of the solder alloy. Brittle interfacial fractures can be more easily achieved by high-speed shear test, especially in higher shear speed. These were discussed with the strengthening mechanism of the solder materials by density and mobility of dislocations. Shear force decreased with shear height, and it could be found that excessively high shear heights unfavorably affected the test results leading to unexpectedly high standard deviation values or shear tip sliding from the solder ball surface.

Formability of Ultrafine-Grain Mg Alloy AZ31B at Warm Temperatures

Warm formability of ultrafine-grain (UFG) AZ31B Mg alloy in the range of 150 °C to 311 °C is investigated. Refinement of grain size significantly improves the formability primarily through increasing strain rate sensitivity of flow stress and increasing diffuse quasi-stable flow, as compared with the coarse-grain AZ31B alloy. Strain rate sensitivity increases with increasing temperatures, and seems to be connected with dynamic recovery and grain boundary processes. For fine-grain sizes, twinning is inhibited. At 200 °C and strain rates below 2 × 10−4 s−1, the UFG AZ31B alloy demonstrates a high rate of strain hardening up to a true strain of 0.6, in addition to its high strain rate sensitivity, which is responsible for its enhanced formability. Examination of the microstructure shows that there is competition between dynamic grain growth and grain refinement during deformation at modest warm forming temperatures, the former causing hardening and the latter causing softening. Increasing the test strain rate and starting with larger grain size initiates deformation twinning during forming, and assists in the refinement of the coarser grains followed by recrystallization.

Enhanced tensile ductility in an electrodeposited nanocrystalline copper

A fully dense nanocrystalline (nc) Cu with mean grain size of 72 nm and a broad grain size distribution was synthesized by electrodeposition. Uniaxial tensile tests were done at different strain rates and room temperature. A very high strength of 1.04 G was obtained at strain rate of 0.1 s−1. The nearly perfect plasticity with a large strain of close to 20% was displayed at specific low strain rates of 4 × 10−5 to 10−4 s−1. With increasing strain rate, the nearly perfect plasticity disappeared. Strain rate sensitivity and activation volume of the nc Cu were estimated from the flow stress at a fixed strain of 1% and a strain rate change (jump) test. It was deduced from the high strain rate sensitivity exponent of 0.08 and small activation volume of 12b3 that both dislocation and grain boundary activities would take place in this nc Cu, which explained the nearly perfect plasticity observed in the tensile test.

High-Temperature Deformation and Ductility of a Modified 5083 Al Alloy

The high-temperature deformation of a 5.5% Mg and 0.6% Ca modified 5083 aluminum alloy was investigated in the temperature range from 573 to 723 K at strain rates in the range of 10−5-10−1 s−1. Ca was added to form an insoluble second phase in the range of temperatures tested to improve the high-temperature characteristics of this alloy. It was shown that the deformation behavior of the alloy could be divided into two regions with stress exponent, n of 3.5 and 13 at low and high strain rates, respectively. The apparent activation energy determined in both regions suggested that the deformation process is diffusion controlled in both regions. The slightly high value of n at the low-strain rate region (viscous glide) was attributed to the presence of threshold stress. The values of threshold stress showed an exponential increase with decreasing temperature and a dependence with an energy term Qo = 16.5 kJ mol−1. Analysis of creep data in terms of threshold stress and using diffusivity of Mg in normalizing the strain rates, revealed two types of deformation behavior. At high values of normalized strain rate $$ ({\ifmmode\expandafter\dot\else\expandafter\.\fi{\upvarepsilon }kT} \mathord{\left/ {\vphantom {{\ifmmode\expandafter\dot\else\expandafter\.\fi{\varepsilon }kT} {DGb}}} \right. \kern-\nulldelimiterspace} {DGb} > 10^{{ - 9}} ), $$ a high value of stress exponent of n = 10 is observed, and the exponential law creep takes place. At low normalized strain rates ≤10−9, the n value is 3 and the true activation energy, Q, is equal to 123 kJ mol−1 suggesting viscous glide of dislocations as rate-controlling mechanism. Enhanced ductility has been observed in the region of viscous-glide controlled deformation as a result of high strain-rate sensitivity.

Dynamic Tensile Properties of TiCp/Ti Composite

The tensile properties of a titanium alloy reinforced with 3% by volume fraction of TiC particles and of an unreinforced titanium alloy are studied over a range of strain rates from 0.0001s-1 to 1300s-1 using quasi-static material testing system (MTS810) and split Hopkinson tensile bar apparatus. The experimental results show that both the TiCp/Ti composite and its matrix alloy exhibit an obvious strain-rate hardening property. But the high strain-rate sensitivity of the TiCp/Ti composite is significantly higher than that of the matrix. The high strain-rate sensitivity of the TiCp/Ti composite is considered to be originated from the high dislocation accumulation rate during dynamic deformation and the constraint of TiC particles on the surrounding matrix, which dramatically enhances rate of the matrix. Finally, a phenomenological dynamic constitutive relation is established considering the composite is elastic-perfectly plastic material.

Impact toughness properties of nickel-free austenitic stainless steels

The Charpy-V impact toughness of six interstitially-alloyed nickel-free austenitic stainless steels was investigated in the temperature range between −196 and 150 °C. Unlike traditional face-centered-cubic steels, the investigated alloys show a marked decrease in impact toughness with decreasing temperature and cleavage-like fracture surfaces at low temperatures. The decrease in impact toughness is due to the combined effects of high strain rate and temperature sensitivity of plastic flow and the strong planarity of the deformation mechanisms of nitrogen-alloyed nickel-free alloys at low temperatures. The effects of the high strain rate and temperature sensitivity of the flow stress on the fracture behavior are discussed based on an analysis of the critical stress for fracture and plastic flow.

The High-Speed Deformation Behavior of TRIP Steels

The high-speed deformation behavior of TRIP steel was investigated at strain rates ranging from 10−2 s−1 to 103 s−1. The effects of metallurgical factors, such as the rolling direction, thickness, and gage length, on the tensile properties at various strain rates were evaluated. The ultimate tensile strength, uniform elongation, strain rate sensitivity, absorbed energy, and strain-hardening exponent are reported. In general, the strength increases and the ductility decreases as the strain rate increases. The samples with a high amount of retained austenite had two distinct regions of strain rate sensitivity, showing high strain rate sensitivity over a strain rate of 102 s−1. The tensile properties were not affected by the gage length and thickness of the tensile samples; however, the rolling direction of the tensile samples affected the UTS values slightly. The absorbed energy of the TRIP steel greatly exceeded that of HSLA steel.

Freeze casting of porous hydroxyapatite scaffolds. II. Sintering, microstructure, and mechanical behavior

In Part I, the influence of processing parameters on the general microstructure of freeze-cast hydroxyapatite (HA) constructs was explored. This work is an extension of Part I to investigate the effect of sintering conditions on the microstructure and mechanical behavior of freeze-cast HA. For constructs prepared from aqueous suspensions (5-20 vol % HA), sintering for 3 h at temperatures from 1250 degrees C to 1375 degrees C produced a decrease in porosity of <5% but an increase in strength of nearly 50%. Constructs with a porosity of 52% had compressive strengths of 12 +/- 1 MPa and 5 +/- 1 MPa in the directions parallel and perpendicular to the freezing direction, respectively. The mechanical response showed high strain tolerance (5-10% at the maximum stress), high strain to failure (>20%), and high strain rate sensitivity. Manipulation of the freeze-cast microstructure, achieved by additions of glycerol and 1,4-dioxane to the aqueous suspensions, produced changes in the magnitude of the mechanical response, but little change in the general nature of the response. The favorable mechanical behavior of the porous constructs, coupled with the ability to modify their microstructure, indicates the potential of the present freeze-casting route for the production of porous scaffolds for bone tissue engineering.