PSI - Issue 60

Vaibhav Gangwar et al. / Procedia Structural Integrity 60 (2024) 123–135 Vaibhav Gangwar / StructuralIntegrityProcedia00(2024)000 – 000

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(P. K.C. Wood et al. 2007a; Paul K C Wood et al. 2014).The limitation in traditional test setup like INSTRON 5582 or INSTRON 8801 was the extensometer used lost its structural integrity above strain rate 1 s -1 and when testing at extremely high speeds, the extensometer response would not be quick enough. Non-contact types of extensometers are available nowadays like Electro-optical, Doppler, and laser extensometers. Material elongation is measured by capturing the image by high-speed cameras and processing in Digital image Correlation (DIC).Although the method is quite reliable but the cost of conducting a single experiment is very high. The most accurate way to measure strain is to attach a strain gauge to the specimen gauge section. This study aims to explore the acceptability of tensile test results at a high strain rate conducted in INSTRON CEAST 9350 drop weight impact testing. The data is compared with the results of equivalent strain rate obtained from servo-hydraulic test setup employed with DIC. Then numerical simulation is performed by using MJC material model. The material parameters for MJC material model are extracted from both the data. The validity of the parameters is verified by numerical simulation of Charpy impact test. 2. Modified Johnson-cook material model Despite being well-known for quasi-static or dynamic loading, the J-C model(Johnson and Cook 1983) does not permit the definition of the entire field of strain rates between quasi-static and dynamic loading. Since the strain rate sensitivity is linear and the strain hardening exponent is temperature-independent, the formulation is primarily to blame for this(Olivier Pantale et al. 2018). As a result, a modified Johnson-Cook constitutive relation is proposed for this type of material to reproduce material response seen in the quasi-static and dynamic range. This modification is based on conventional plasticity theory (Banerjee et al. 2015). This computational model's equivalent flow stress is expressed as the following function of the equivalent plastic strain, strain rate, and temperature. ( , ̇ ,T) = [A+B ] [ 1 + 2 ( ̇ ̇ ) ][1- 3 ∗ ] (1) Where A, B, G 1 , r, G 2 , G 3 , m are material constants, in this model the strain hardening exponent is also dependent upon temperature: n = 1-G 4 (2) G 4 isalso a material constant. The equation for homologous temperature, T * = (T w -T room )/(T melt -T room ) is same as in the J-C model. Y = A+B (3) = Y × [ 1 + 2 ( ̇ ̇ ) ] (4) from Eq.(4) values of parameters 1 , 2 and r determined from fitting curve at each corresponding strain rate as shown in Fig.9(a). K = [A+B ] [ 1 + 2 ( ̇ ̇ ) ] (5) ( , ̇ ,T) = K × [1- 3 ∗ ] (6) By Curve fitting Eq. (6), can be used to determine the parameters G 3 and m. In Eq. (1), the expression in the first bracket denotes strain hardening that is temperature dependent, the expression in the second bracket denotes strain rate sensitivity that is non-linear, and the expression in the third bracket denotes exponential temperature sensitivity. This suggests a dependence between strain hardening, strain-rate hardening, and temperature softening (i.e., the coupling effect persists as in the J-C model). All three of these are changed. The model is more flexible because of the eight additional material constants, but their determination is still very simple with a few additional experimental data. From the already available experimental results, all new parameters can be derived. The method for extracting parameters is the same as for the J-C model. In ABAQUS standard software, the model is implemented using a UMAT (user-defined material model). Tables 1 and 2 contain a list of the parameter values. 3.Tensile test in Drop weight Impact testing machine: High strain rate stress-strain data is a crucial component of the material inputs for precise computer prediction. The tensile tests at four velocities in INSTRON CEAST 9350 Impact test set up are conducted at room temperature by employing strain gage to measure sample displacement. Before this calibration of strain gauge is necessary.