Applicability of constitutive models of Cowper–Symonds (CS), Modified Cowper–Symonds (Modified CS), Johnson–Cook (JC), Zerilli–Armstrong (ZA) and Tanimura–Mimura 2009 (TM2009) is discussed by ...comparing the properties of these models with experimental data. It is shown that the stress–strain curves at each strain rate, which are predicted by using the values of parameters published in the literature for the CS, MCS, JC and ZA models, can sometimes diverge from the experimental curves, not only for the large strain region near the true fracture strain, but also for the homogenous deformation region. It is only necessary to know the quasi-static stress–strain curve in advance for the TM 2009 model, because the set of parameters is given for each material group, and can be used for any material belonging to the group. Simple methods to estimate the quasi-static curve are discussed.
This study addressed to determine the flexural properties of hybrid composite laminates (HCAFRE) under the strain rate sensitivity. The hybrid composite laminate was formed as consecutive stacking of ...a sequence of plain woven carbon fiber reinforced epoxy (CFRE) and a plain-woven aramid fiber reinforced epoxy (AFRE) laminates. The flexural tests were carried out at four different strain rates (0.01, 0.11, 0.55, 1.1 s−1) to determine the strain rate sensitivity of the HCAFRE. Moreover, the strain rate sensitivity of CFRE and AFRE was also determined individually. The effect of different fiber orientations (0°, 45°, and 90°) on the flexural properties of the composite laminates were also investigated at the scope of this study. In numerical analysis, composite laminates (CFRE, AFRE, and HCAFRE) were constituted in LS-DYNA finite element program using the Cowper-Symonds material model (MAT 112) which includes strain rate dependency. Consequently, it was seen that the experimental and numerical results were indicated a similar tendency to each other. Therefore, it was understood that the Cowper-Symonds material model is suited for the flexural behavior model of composite laminates under different strain rates.
Civil infrastructure systems such as bridge piers, navigational guide walls, and protection structures that are located near navigable waterways are inherently at risk for being impacted by cargo ...vessels such as barges and ships. To safely design such systems to possess adequate vessel impact resistance, structural loads associated with potential vessel-structure collision conditions must be quantified in a conservative manner. While high-resolution finite element impact simulations may be employed to compute such loads, care must be exercised in defining the material characteristics of the vessel if conservative structural design loads are to be obtained. Importantly, constitutive relationships assigned to steel components in the vessel model must be capable of accounting for strain rate sensitivities and large-scale plastic deformations.
In the present study, strain rate sensitive constitutive models were developed for two types of steel commonly utilized in marine construction in the United States—ASTM A36 and ASTM A1011. Tension tests were conducted over a wide range of strain rates (7.00 × 10−5 s−1 – 250 s−1) spanning from quasi-static to intermediate and high rates that are typically associated with vessel-structure impact events. A novel testing apparatus—employing an impact pendulum as an energy supply mechanism—was designed for this study to conduct intermediate to high-rate material testing. Features of the apparatus, discussed in this paper, overcome key problems encountered in other studies that have employed impact loading for tensile material testing. From the testing program, representative stress–strain relations and Cowper–Symonds strain rate sensitivity parameters were developed for the materials tested. Rate sensitivities of the two steel grades tested were found to be very similar to each other. Additionally, rate sensitivities from the present study agreed well with ultimate stress data measured in past studies of mild steel, but were found to be less rate-sensitive than yield stress data measured in past studies.
•A novel impact-based high strain rate test apparatus was developed and employed.•A36 and A1011 specimens were tested in tension over a wide range of strain rates.•Rate-sensitive constitutive models were developed and implemented in LS-DYNA.•System-level demonstration was performed using impact testing and finite element analysis.
This paper presents a new formula for prediction of the dynamic hardening effect for various marine structural steels, considering dependencies on the strain rates and temperatures. Dynamic tensile ...tests are carried out for three kinds of marine steels, 2W50, EH36, and DH36, changing the steel layer in the thickness direction, the strain rates, and temperatures. Considering two thickness layers at the middle and surface, five strain rate levels of 0.001/s, 1/s, 10/s, 100/s, and 200/s, three temperature levels of LT (−40 °C), RT, and HT (200 °C), and two repetitions, the total number of tests is 180. Dynamic hardening is clearly seen at LT and RT regardless of the material type, while dynamic strain aging occurs at HT, leads to negative strain rate sensitivity, and thus elevates the quasi-static flow stress above the dynamic flow stress to a certain strain rate. Dynamic hardening factors (DHFs) are derived as a function of the proof strains of 0.05, 0.10, and 0.15 according to each material type and temperature level. A new formula to determine the material constant D of Cowper–Symonds constitutive equation is developed. The correctness of the proposed formula is verified through comparison with test flow stress curves and reference test data in large plastic strain and high strain rate ranges.
•Dynamic tensile tests are carried out for various marine steels.•A new formula for prediction of the dynamic hardening effect is presented.•Various strain rates and temperatures are considered.•Dynamic hardening factors (DHFs) are derived as a function of the plastic strain and strain rate.
Our work studies the dynamic properties of coated and uncoated 2D C/SiC composite material from 173 K to 1273 K by means of Split Hopkinson Tensile Bar. Examination of the failure process of the ...specimen by SIM D8 ultra high-speed camera and damage analysis help define the three phases of crack propagation, namely: the elastic pre-damaged phase, the yielding phase or the crack-initiating phase, and the failure phase or the phase of fast-spreading cracks. Experimental results also reveal that the dynamic tensile strength of both coated and uncoated composites decreases with the increase of temperature and decreases more conspicuously at higher temperature. An SEM is employed to examine the fracture surface and damage of C/SiC composites at different temperatures are determined by calculation. Finally, k was introduced according to the Cowper-Symonds fitting model to describe the temperature dependency. This implies a greater significance of SiC coating on the properties of the composite with the increase of temperature. Thus, it is believed that coated composite within the temperature range of 173 K–1273 K displays a superior impact property compared with uncoated composite, and is a better structural thermal protection material.
In this article, a response of the complex-phase high-strength steel SZBS800 was modelled by considering the strain-rate influence. The material's response was first measured with a series of ...standard tensile tests at lower strain rates. Higher strain rates were achieved using the unconventional test of shooting the ball into flat specimens. A viscoplastic formulation of the Cowper-Symonds material model was applied to consider the strain-rate effects. The parameters
,
, and
of the material model were estimated using a step-wise procedure. First, rough estimates of the three parameters were obtained from the tensile tests using the grid search method. Then, the parameters
and
were fine-tuned using the reverse engineering approach. With the help of explicit dynamic simulations and all the experimental data, a multi-criteria cost function was defined and applied to obtain a smooth response function for the parameters
and
. Its optimum was determined by a real-valued genetic algorithm. The optimal values of the estimated parameters model the material response well, although a domain of optimum candidates spans two orders of magnitude for the parameter
and a few orders of magnitude for the parameter
.
The research presented in this manuscript focuses on the development of an LS-DYNA finite element model to predict the dynamic shear strength of short riveted lap-spliced specimens. Using data ...collected from experimental testing at the U.S. Army Engineer Research and Development Center (ERDC), a finite element model was developed to replicate the behavior of A502 Grade short riveted connections under quasi-static loading. Subsequent analyses used published Cowper-Symonds constitutive model coefficients to replicate the behavior of these connections under dynamic loading. Computed results were then compared with available test data from ERDC. Given the challenges involved in creating physical models with riveted connections and the abundance of historical bridges constructed with rivets, the developed finite element analysis engineering solution can serve as a critical tool for researchers interested in predicting the response of short riveted connections to dynamic loading and those interested in developing strategies to mitigate against this loading.
Complex numerical simulations of tunnels are often used to model effects of high strain rate surface loads. Most of this modeling ignores soil's strength dependency on strain rate to lessen the ...complexity. A series of Split Hopkinson Pressure Bar (SHPB) tests emulates the high strain rate compression occurring in blast events, for Nile Silty Clay (NSC) samples. The Cowper Symonds parameters are calibrated to SHPB test results and are used in advanced three-dimensional finite element analysis of a benchmark tunnel problem using Abaqus/Explicit software. The shallow tunnel in NSC formation is subjected to a blast event at the ground surface simulated by the CONWEP algorithm. The Smoothed Particle Hydrodynamic (SPH) mesh-free technique captures the crater formed due to the explosion. Results from the benchmark problem show that including the strain rate dependency in the analysis leads to a significant reduction in the calculated tunnel liner straining actions and deformations.
Accurately considering the dynamic mechanical properties of rolled thin-walled steel plates (TWSPs) under low and medium strain rates is the basis of numerical simulations of W-beam guardrails ...subjected to vehicle impact. Uniaxial tensile tests were conducted on specimens extracted from different locations (flat TWSPs without cold rolling treatment, and the cross-sectional centers and slopes of rolled TWSPs) and under different strain rates (ε˙ = 0.00025, 0.01, and 50 s−1). Based on experimental and numerical results, the cross-sectional center of a rolled TWSP is recommended as the representative sampling location for uniaxial tensile tests. Additional uniaxial tensile tests with wider strain rates of 10, 100, and 200 s−1 were also conducted on specimens at the recommended sampling location (cross-sectional center) of rolled TWSPs. It was found that the Cowper–Symonds model with parameters of C = 40 s−1 and p = 5 recommend by Symonds significantly overestimated the strain rate effects of the rolled TWSP material in the low and medium strain-rate region. The model with calibrated parameters of C = 4814 s−1 and p = 2.9 was recommended for considering the influences of strain rate effects on the dynamic mechanical properties of rolled TWSP at low to medium strain rates.
In dental implant insertion, an artificial foundation is prepared for the prosthetic device, which involves the surgical positioning of the implant in the jaw bone. The success of dental implants ...relies on the osseointegration process. The biomechanical factors, such as stress and strain, developed during the insertion affect the jawbone and its surroundings. In this current study, the stresses during the implant insertion in the mandibular jawbone bone are analyzed using three-dimensional explicit dynamic analysis, and the Cowper–Symonds model is implemented with the damage model. The implant’s design has a substantial impact on stress distribution within the cancellous bone during the insertion procedure. The stress variation takes place as the implant moves into the pre-drilled hole. This is because of the contact between the bone and the fixture on the implant. The upper edge of the predrilled site shows that the stresses are more at the crestal region of the implant due to surface area. There is a gradual increase in the stress level as the implant reaches the lower edge from the top edge. This is because of the concept of mechanical interlocking. Clinicians can use this information to anticipate and address potential stress-related challenges during implant placement.
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