Rates of Strain

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Magnus Langseth - One of the best experts on this subject based on the ideXlab platform.

  • application of a split hopkinson tension bar in a mutual assessment of experimental tests and numerical predictions
    International Journal of Impact Engineering, 2011
    Co-Authors: Yongjun Chen, A H Clausen, Odd Sture Hopperstad, Magnus Langseth
    Abstract:

    Abstract This paper shows how experimental test results from a split-Hopkinson tension bar (SHTB) and numerical simulations of the test set-up can be used for mutual verification. Firstly, a SHTB where the tension stress wave is generated by pre-stretching a part of the incident bar is briefly presented. This SHTB is used to carry out tensile tests of four aluminium alloys at high Rates of Strain, while tests at low to medium Strain Rates were performed in a servo-hydraulic tensile test machine. Using the test results, the parameters of an anisotropic thermoelastic-thermoviscoplastic constitutive relation and a one-parameter fracture criterion are identified for the materials at hand. Subsequently, the material model is used in explicit finite element analyses of the SHTB tests, including the entire experimental set-up and the stress wave propagation during the test. The numerical predictions were found to represent the observed behaviour in the experimental tests fairly well.

  • stress Strain behaviour of aluminium alloys at a wide range of Strain Rates
    International Journal of Solids and Structures, 2009
    Co-Authors: A H Clausen, Odd Sture Hopperstad, Magnus Langseth
    Abstract:

    Abstract The stress–Strain behaviour of extruded AA6xxx and AA7xxx aluminium alloys in T6 temper was studied at a wide range of Strain Rates. Tensile tests at low to medium Strain Rates were performed in a standard tensile test machine, while a split-Hopkinson tension bar was used to carry out tests at high Rates of Strain. Extruded aluminium alloys have anisotropic mechanical properties, and tests were therefore done in three directions with respect to the extrusion direction. It is found that the AA6xxx alloys exhibit no significant rate sensitivity in the stress–Strain behaviour, while moderate rate sensitivity was found for the AA7xxx alloys. There seems to be no significant difference between the rate sensitivity in the three tensile directions. The experimental data were used to identify the parameters of a thermo-viscoplastic constitutive relation for the extruded alloys, which includes the effects of Strain hardening, Strain-rate hardening, thermal softening and plastic anisotropy.

  • A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis
    International Journal of Solids and Structures, 2008
    Co-Authors: V. Tarigopula, A H Clausen, Magnus Langseth, Odd Sture Hopperstad, François Hild
    Abstract:

    Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a Strain-rate in the range of 150-600/s and in a servo-hydraulic testing machine at a Strain-rate between 10-3 and 100/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study Strain localisation in the tensile specimens at high Rates of Strain. By using digital image correlation, it is possible to obtain in-plane displacement and Strain fields during non-uniform deformation of the gauge section, and accordingly the Strains associated with diffuse and localised necking may be determined. The full-field measurements in high Strain-rate tests reveal that Strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress-Strain behaviour and Strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress-Strain behaviour, deformed geometry and Strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.

J Harding - One of the best experts on this subject based on the ideXlab platform.

  • deformation of thermosetting resins at impact Rates of Strain part 2 constitutive model with rejuvenation
    Journal of The Mechanics and Physics of Solids, 2004
    Co-Authors: C.p. Buckley, J Harding, P J Dooling, C. Ruiz
    Abstract:

    Abstract The constitutive responses of three glassy thermoset polymers at impact Rates of Strain and slower, together with measurements of adiabatic heating, were reported earlier by the authors. The results are interpreted here in the context of a constitutive model proposed previously for amorphous polymers, expanded to incorporate Strain-softening and the adiabatic heating deficit. In terms of the model, both features are a natural consequence of Strain-induced evolution of the glass structure, as represented by Tool's “fictive temperature”—the phenomenon of structural rejuvenation. A representation is proposed for the evolution of fictive temperature with plastic Strain, motivated by an approximate treatment of the kinetics of physical ageing/rejuvenation. Formulated in this manner, the model agrees reasonably well with experimental results across the wide range of Strain Rates of the previous experiments, 10−3 to 4.5×10 3 s −1 , and across most of the range of Strain to failure in compression. At the highest Strains, however, an additional adiabatic heating deficit appears that is not predicted by the model, either suggesting the onset of structural breakdown possibly associated with the appearance of cracks or reflecting a need for better physical understanding of large deformations in glassy polymers.

  • Deformation of thermosetting resins at impact Rates of Strain. Part I: Experimental study
    Journal of The Mechanics and Physics of Solids, 2001
    Co-Authors: C.p. Buckley, J Harding, C. Ruiz, A Trojanowski
    Abstract:

    Abstract Three thermosetting resins have been tested in compression at Strain Rates between 10 −3 and 5×10 3 s −1 . A smaller number of tests have been performed on the same resins at similar Strain Rates in tension. The testing technique is described and the results obtained are presented. Significant differences between the three materials were found over the whole range of Strain Rates. All three exhibited a pronounced Strain rate sensitivity. Temperature measurements, performed in compression tests at the higher Strain Rates, showed evidence of adiabatic heating. This revealed the presence of energy storage mechanisms in both yield and Strain–stiffening regimes.

  • the effect of Strain rate on the through thickness tensile stiffness and strength properties of fibre reinforced epoxy composites
    Journal De Physique Iv, 2000
    Co-Authors: J L Medina, J Harding
    Abstract:

    An experimental technique is described for determining the through-thickness stiffness and strength properties of laminated composites at impact Rates of Strain. Results are presented for through-thickness tensile tests on a X-ply CFRP, a woven CFRP and a woven GFRP at a quasi-static, an intermediate and an impact rate of Strain. A small increase in strength and failure Strain is observed under impact loading but tensile modulus and Poisson's ratio are essentially independent of Strain rate.

  • a constitutive relation and failure criterion for ti6al4v alloy at impact Rates of Strain
    Journal of The Mechanics and Physics of Solids, 1999
    Co-Authors: D A S Macdougall, J Harding
    Abstract:

    Abstract Shear stress-Strain curves have been obtained for thin-walled tubular specimens of Ti6Al4V alloy at Strain Rates from ∼7×10−4/s to ∼1000/s. A specially developed infrared radiometer has been used to measure the rise in specimen surface temperature during the high Strain rate tests where the deformation process is essentially adiabatic. The data obtained were used to obtain material constants for a Zerilli–Armstrong type constitutive relation giving the best fit with the observed mechanical response. This relation was incorporated in the ABAQUS/explicit FE code and shown to predict the experimentally measured flow stress in the impact tests with reasonable accuracy. A failure criterion, based on a critical value of effective plastic Strain, is also incorporated, the critical condition being chosen to give agreement between the predicted and the measured overall failure Strains. The validity of the constitutive relation and associated failure criterion is then assessed in terms of their ability to predict the observed mechanical response in tensile impact tests on specimens of both cylindrical and rectangular cross-section where the early onset of localised plastic flow and significant temperature rises in this region provide a more rigorous test of the proposed model. High-speed photography was used to monitor the changing specimen cross-section and the infrared radiometer was used to determine the specimen surface temperature in the region of localised deformation. Reasonable agreement was obtained between the experimental results and the numerical predictions using the ABAQUS/explicit FE code.

  • determination of interlaminar shear strength for glass epoxy and carbon epoxy laminates at impact Rates of Strain
    Composites Science and Technology, 1992
    Co-Authors: J Harding, Y L Li
    Abstract:

    Abstract A brief review is given of some of the techniques which have been used to determine the interlaminar shear strength of laminated composites under impact loading. A new technique employing a double-lap shear specimen, where failure occurs on predetermined interfaces, is then described and results are presented for tests on this design of specimen at both a quasi-static and an impact rate of Strain. The Strain distribution along the failure plane is determined by using a finite element analysis. Large variations in both the shear Strain and the normal Strain were observed, the magnitude of this variation being sensitive both to the elastic properties of the different reinforcing plies and to the chosen stacking sequence. Results are presented for the interlaminar shear strength at the interface between (a) two plain-weave glass/epoxy plies, (b) two plain-weave carbon/epoxy plies, and (c) a plain-weave glass/epoxy and a plain-weave carbon/epoxy ply. In each case the mean value of the interlaminar shear stress at failure was found to increase significantly as the loading rate was raised from quasi-static to impact.

Clive R. Siviour - One of the best experts on this subject based on the ideXlab platform.

  • the effect of Strain rate specimen geometry and lubrication on responses of aluminium aa2024 in uniaxial compression experiments
    Experimental Mechanics, 2009
    Co-Authors: Peifeng Li, Clive R. Siviour, Nik Petrinic
    Abstract:

    The ability to observe and quantify intrinsic material response to loading at different Rates of Strain has been improved by reducing the errors of mechanical characterisation in uniaxial compression experiments. In order to perform comparisons of the results from uniaxial compression tests used to characterise mechanical properties of aluminium alloys at different Strain Rates, it is necessary to reduce errors resulting from factors such as specimen design. In this study, the effects of Strain rate, specimen geometry and lubrication on the compressive properties of aluminium AA2024 alloy were quantitatively investigated by measuring the mechanical behaviour of this alloy as functions of Strain rate, specimen aspect ratio and lubrication condition. Both the deformation history and the failure mode were identified using low and ultrahigh speed photography. The interaction of factors influencing the measured stress-Strain response was quantified, and suitable specimen aspect ratios for compression tests at different Strain Rates were identified.

  • Mechanical properties of SnPb and lead-free solders at high Rates of Strain
    Journal of Physics D: Applied Physics, 2005
    Co-Authors: Clive R. Siviour, Stephen M. Walley, William G. Proud, J E Field
    Abstract:

    The mechanical properties of 63% Sn–37% Pb and lead-free solders have been measured at high Strain Rates (500–3000 s −1 ) using a split Hopkinson pressure bar. The solders were produced by quenching in water from the melt, to give the phase structure associated with rapid cooling. Measurements were made at −40 °C, room temperature and +60 °C. The Sn–Pb solder was strongly Strain rate and temperature dependent, whereas the lead-free solders showed only a weak dependence on these parameters. All of the materials behaved elasto-plastically until a plateau stress of circa 200 MPa. An unexpected, and possibly important, feature of the lead-free solders was the division of the specimens into two groups with different strengths at low temperatures.

  • Review of experimental techniques for high rate deformation and shock studies
    International Journal of Impact Engineering, 2004
    Co-Authors: John E. Field, William G. Proud, S. M. Walley, H.t. Goldrein, Clive R. Siviour
    Abstract:

    Abstract A variety of techniques used to obtain the mechanical properties of materials at high Rates of Strain (⩾10 s−1) are summarised. These include dropweight machines, split Hopkinson pressure bars, Taylor impact and shock loading by plate impact. High-speed photography, particularly when used in association with optical techniques, is a key area and recent advances and applications to studies of ballistic impact are discussed. More comprehensive bibliographies and a fuller discussion of the history may be found in earlier reviews published by us in 1994, 1998 and 2001 (J Phys IV France 4 (C8) (1994) 3; Review of experimental techniques for high rate deformation studies, Proceedings of the Acoustics and Vibration Asia ’98, Acoustics and Vibration Asia 98 Conference, Singapore, 1998; Review of experimental techniques for high rate deformation and shock studies, New Experimental Methods in Material Dynamics and Impact, Institute of Fundamental Technological Research, Warsaw, Poland, 2001).

Katherine J Kendrick - One of the best experts on this subject based on the ideXlab platform.

  • latest pleistocene and holocene slip rate for the san bernardino strand of the san andreas fault plunge creek southern california implications for Strain partitioning within the southern san andreas fault system for the last 35 k y
    Geological Society of America Bulletin, 2013
    Co-Authors: Sally F Mcgill, Lewis A Owen, Ray J Weldon, Katherine J Kendrick
    Abstract:

    An alluvial succession on the northeast side of the San Bernardino strand of the San Andreas fault includes distinctive aggradational and degradational features that can be matched with correlative features on the southwest side of the fault. Key among these are (1) a terrace riser on the northeast side of the fault that correlates with an offset channel wall on the southwest side of the fault and forms a basis for slip estimates for the period ca. 35 ka to the present, and (2) a small alluvial fan on the southwest side of the fault that has been matched with its most likely source gullies on the northeast side of the fault and forms a basis for slip estimates for the last 10.5 k.y. Slip-rate estimates for these two separate intervals are nearly identical. The rate for the older feature is most likely between 8.3 and 14.5 mm/yr, with a 95% confidence interval of 7.0–15.7 mm/yr. The rate for the younger feature is most likely between 6.8 and 16.3 mm/yr, with a 95% confidence interval of 6.3–18.5 mm/yr. These Rates are only half the previously published slip rate for the San Andreas fault 35 km to the northwest in Cajon Pass, a rate that traditionally is extrapolated southeastward along the San Bernardino section of the fault. Results from Plunge Creek suggest that about half of the 25 mm/yr rate at Cajon Pass transfers southeastward to the San Jacinto fault, as proposed by other workers on the basis of regional geologic relations. These results indicate that the discrepancy between latest Quaternary slip Rates and present-day Rates of Strain accumulation across the San Bernardino section of the San Andreas fault from geodesy can be largely explained by slip transfer between faults, leading to spatial variation in rate along the San Andreas fault. Nonetheless, the latest Pleistocene and Holocene slip rate at Plunge Creek is still somewhat faster than Rates inferred for the San Bernardino section of the San Andreas fault based on elastic block modeling of geodetic data and may be more appropriate than those Rates for hazard estimation.

C.p. Buckley - One of the best experts on this subject based on the ideXlab platform.

  • deformation of thermosetting resins at impact Rates of Strain part 2 constitutive model with rejuvenation
    Journal of The Mechanics and Physics of Solids, 2004
    Co-Authors: C.p. Buckley, J Harding, P J Dooling, C. Ruiz
    Abstract:

    Abstract The constitutive responses of three glassy thermoset polymers at impact Rates of Strain and slower, together with measurements of adiabatic heating, were reported earlier by the authors. The results are interpreted here in the context of a constitutive model proposed previously for amorphous polymers, expanded to incorporate Strain-softening and the adiabatic heating deficit. In terms of the model, both features are a natural consequence of Strain-induced evolution of the glass structure, as represented by Tool's “fictive temperature”—the phenomenon of structural rejuvenation. A representation is proposed for the evolution of fictive temperature with plastic Strain, motivated by an approximate treatment of the kinetics of physical ageing/rejuvenation. Formulated in this manner, the model agrees reasonably well with experimental results across the wide range of Strain Rates of the previous experiments, 10−3 to 4.5×10 3 s −1 , and across most of the range of Strain to failure in compression. At the highest Strains, however, an additional adiabatic heating deficit appears that is not predicted by the model, either suggesting the onset of structural breakdown possibly associated with the appearance of cracks or reflecting a need for better physical understanding of large deformations in glassy polymers.

  • Deformation of thermosetting resins at impact Rates of Strain. Part I: Experimental study
    Journal of The Mechanics and Physics of Solids, 2001
    Co-Authors: C.p. Buckley, J Harding, C. Ruiz, A Trojanowski
    Abstract:

    Abstract Three thermosetting resins have been tested in compression at Strain Rates between 10 −3 and 5×10 3 s −1 . A smaller number of tests have been performed on the same resins at similar Strain Rates in tension. The testing technique is described and the results obtained are presented. Significant differences between the three materials were found over the whole range of Strain Rates. All three exhibited a pronounced Strain rate sensitivity. Temperature measurements, performed in compression tests at the higher Strain Rates, showed evidence of adiabatic heating. This revealed the presence of energy storage mechanisms in both yield and Strain–stiffening regimes.