PSI - Issue 14

Hemant Chouhan et al. / Procedia Structural Integrity 14 (2019) 830–838 Author name / Structural Integrity Procedia 00 (2018) 000–000

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values of rate-dependent parameters for different materials. After an initial elastic loading, a material curve is bound to follow a plastic deformation. Hence, if a power law model alone is not capable of revealing the complete material behavior than another modeling scheme needs to be incorporated, to reveal the true material behavior. The Cowper and Symonds model takes the form of Eq. (5), where A is the yield stress at zero plastic strain, B is the strain hardening coefficient, n is the strain hardening exponent and D and q are strain rate hardening coefficients as discussed by Peroni et al. (2012). This equation has been used repeatedly to describe the plastic behavior of materials assessed using the SHPB technique for different materials, which offers the most general description of a viscoelastic material.  =(A+B  n )[ 1 + ( ̇ � ) �/� ] (5) On attaining the state of equilibrium or peak of stress or strain a simultaneous effect of both the elastic and plastic deformation is inevitable. Therefore, a mathematical term capable of representing the individual and simultaneous effect of strain and strain rate on material behaviour is a necessity. Therefore, the authors propose a phenomenological model by surface fitting the stress-strain rate response. The model uses the SHPB test data till the stress reaches the maxima. Being a phenomenological model the accuracy of the model can only be claimed with in the experimental regions.  = [��� �  � � �� ] + [��� � ̇ � � �� ] + � [���  � � �� ][��� ̇ � � �� ] (6) TableCurve 3D software was used to surface fit the experimental data of Fig. 3, the resulting surface plot is presented in Fig. 4. A correlation coefficient (r 2 ) of 0.9704 and 0.9136 is obtained for this fit on the dry and wet composite. The best fit was due to Eq. (6) (fitting parameters in Table 2), in which the stress is related to strain and strain rate which are raised to a constant power. The first term represents the elastic behavior, the second term the rate dependent plastic deformation and the third is a cross term combining the two.

Table 2. Surface fitting parameters for dry and wet UHMWPE-SR composite.

Model Parameter

Model parameter

Dry UHMWPE-SR

Wet UHMWPE-SR

a b c d e

17.3345 0.0195 -1.1361 819.6964 7849.22 1.8806 2269.82 0.9704 0.9699

201.3983 0.0133 1.0516 14.9765 2767.58 0.0961 -2.6501 0.9136 0.9194

f

g

r 2

Adjusted r 2