PSI - Issue 14

Kartikeya et al. / Procedia Structural Integrity 14 (2019) 514–520 Kartikeya/ Structural Integrity Procedia 00 (2018) 000 – 000

516

3

(2)

Johnson and Cook Damage model specifies damage initiation in the material as given by Eq. 3. Strain at fracture could be shown to depend upon stress-triaxiality ratio, strain rate and temperature change. In Eq. 3, terms in the first parenthesis signifies strain to fracture which decreases as hydrostatic tension increases, the second parenthesis signifies the effect of increased strain rate on material ductility and the third parenthesis signifies effect of thermal softening.

(3)

Where

is the stress-triaxiality ratio.

Johnson-Cook material parameters for ARMOX 407T Steel are reported recently in the literature by Mehreganian (2018) and are reproduced here in Table 1.

Table 1. Johnson-Cook material parameters for ARMOX 440T Steel. Parameter Unit

Value

Quasi-Static Yield Stress, A

MPa MPa

1210 1543 0.584 1 0.014

Hardening Constant, B

Hardening Exponent, n Reference Strain Rate, Epsilon dot zero Strain-Rate Strengthening Coefficient, C

- - -

2.2. Finite Element Model

Commercial Finite Element Package Abaqus 2017 is used for the current study. Steel plate is modeled as deformable solid with dimensions of 400mm x 400mm x 4.6mm as shown in Table 2. For a plate, dimensions in two directions are much larger than in thickness direction. When loading is applied to a thin plate it responds by bending and membrane stretching i.e. no stresses in thickness direction. Given the topology of a shell element, degrees of freedom are activated in only two directions considering the phenomenon in thickness direction is trivial to problem. Plate was meshed with brick, shell and continuum shell elements. Shell elements are computationally economical and they capture response well in the plate bending problems. Solid elements and continuum shell elements have similar topology. For solid elements to capture the response in bending, number of elements in the thickness direction need to be increased which makes them computationally expensive. Continuum shell elements can be considered as the best of both solid and shell worlds in bending problem as they possess geometry of solid element but are based on shell theories. Air-Blast generates spherical incident waves, whereas, surface-blast generates hemispherical incident waves that propagate through the available medium. Detonation of landmine and buried IEDs are essentially surface blasts, whereas, any explosion open to atmosphere is air-blast. Abaqus provides a convenient method, CONWEP (which stands for conventional weapon) for simulating pressure wave by detonation of an explosive for both air and surface blast. CONWEP requires input of distance of loading surface from source of detonation and equivalent amount of TNT for explosive. It calculates maximum overpressure (above ambient), the arrival time, the positive phase duration and the exponential decay coefficient for both incident pressure and reflected waves. Incident pressure on a surface can be defined as a function of time and angle between normal to surface and vector between surface and source as shown in Eq. 4.