ABAQUS User Subroutine Development for Energy Releasing Rate of the Functionally Graded Plate with Cracks

doi:10.12068/j.issn.1005-3026.2017.09.020

Abstract

Abstract: To obtain the dynamic energy releasing rate of the functionally graded plate with cracks， a virtual crack closure technique was proposed based on the inhomogeneous finite element method. A fracture dummy node element of the functionally graded material under dynamic loading was developed， user-defined subroutines named UMAT and UEL were programmed， and the component of energy releasing rate for the functionally graded plate caused by dynamic loading was calculated based on the finite element software ABAQUS platform. For the different shape factors such as the center-crack and inclined-crack inside the functionally graded plates， the component of the dynamic energy releasing rate was solved， and then it was transformed into the dynamic stress intensity factor， which was used for comparing the results calculated by the finite difference method. The numerical calculating results showed that the dummy node element of the functionally graded material fracture caused by dynamic loading is characterized by high precision， simplicity and convenience without using the singular element or special element for the crack tip and the versatility of its subroutines， which may provide a new approach for the engineers to get the dynamic fracture parameters.

Key words: crack, dynamic energy releasing rate, virtual crack closure technique, dynamic stress intensity factor, inhomogeneous finite element method

CLC Number:

TB115

ZHOU Li-ming， REN Shu-hui， MENG Guang-wei， LI Rong-jia. ABAQUS User Subroutine Development for Energy Releasing Rate of the Functionally Graded Plate with Cracks[J]. Journal of Northeastern University Natural Science, 2017, 38(9): 1309-1314.

References

[1]Xie D，Biggers S B.Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique［J］.International Journal of Impact Engineering，2007，34(6):1047-1060.
[2]Xie D，Biggers S B.Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique.part I:formulation and validation［J］.Engineering Fracture Mechanics， 2006，73(6):771-785.
[3]Wimmer G，Schuecker C，Pettermann H E.Numerical simulation of delamination in laminated composite components—a combination of a strength criterion and fracture mechanics［J］.Composites Part B:Engineering，2009，40(2):158-165.
[4]Sundaram B M，Tippur H V.Dynamic crack growth normal to an interface in bi-layered materials:an experimental study using digital gradient sensing technique［J］.Experimental Mechanics，2016，56(1):37-57.
[5]Ahmed A，Sluys L J.A computational model for the simulation of dynamic fracture in laminated composite plates［J］.Journal of Composite Materials，2015，49(14):1717-1738.
[6]Msekh M A，Sargado J M，Jamshidian M，et al.Abaqus implementation of phase-field model for brittle fracture［J］.Computational Materials Science，2015，96(Part B):472-484.
[7]Wang Z，Li P.Dynamic failure and fracture mechanism in alumina ceramics:experimental observations and finite element modelling［J］.Ceramics International，2015，41(10):12763-12772.
[8]Bagheri R，Fard K M，Monfared M M.Dynamic fracture analysis in an orthotropic half-plane with FGM coating containing several moving cracks［J］.Acta Mechanica，2015，226(6):1725-1736.
[9]Monfared M M，Ayatollahi M.Dynamic stress intensity factors of multiple cracks in an orthotropic strip with FGM coating［J］.Engineering Fracture Mechanics，2013，109:45-57.
[10]Manolis G D，Dineva P S，Rangelov T V.Dynamic fracture analysis of a smoothly inhomogeneous plane containing defects by BEM［J］.Engineering Analysis with Boundary Elements，2012，36(5):727-737.
[11]Lee K H.Analysis of a propagating crack tip in orthotropic functionally graded materials［J］.Composites Part B:Engineering，2016，84(2):83-97.
[12]Abdollahifar A，Nami M R.Determination of dynamic stress intensity factor in FGM plates by MLPG method［J］.IJST，Transactions of Mechanical Engineering， 2014，38(M1):181-194.
[13]Rouzegar S J，Mirzaei M.Modeling dynamic fracture in Kirchhoff plates and shells using the extended finite element method［J］.Scientia Iranica，2013，20(1):120-130.
[14]Bui T Q.Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS［J］.Computer Methods in Applied Mechanics and Engineering，2015，295:470-509.
[15]Zhao W，Hu Z，Zhang X，et al.The dynamic stress intensity factor around the anti-plane crack in an infinite strip functionally graded material under impact loading［J］.Theoretical and Applied Fracture Mechanics，2014，74:1-6.
[16]Bhardwaj G，Singh I V，Mishra B K，et al.Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions［J］.Composite Structures，2015，126:347-359.
[17]C，eribas，s S.Static and dynamic analyses of thin uniformly loaded super elliptical FGM plates［J］.Mechanics of Advanced Materials and Structures，2012，19(5):323-335.