THE CALIBRATION OF MICRODEFECTS INDUCED EQUIVALENT DAMAGE AREA/VOLUME OF BRITTLE MATERIALS BY USING THE M-INTEGRAL

Zhu Wenjie; Lü Junnan; Li Qun

doi:10.6052/0459-1879-17-378

Volume 50 Issue 2

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Chinese Journal of Theoretical and Applied Mechanics > 2018 > 50(2): 297-306. > DOI: 10.6052/0459-1879-17-378 CSTR: 32045.14.0459-1879-17-378

Zhu Wenjie, Lü Junnan, Li Qun. THE CALIBRATION OF MICRODEFECTS INDUCED EQUIVALENT DAMAGE AREA/VOLUME OF BRITTLE MATERIALS BY USING THE M-INTEGRAL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 297-306. DOI: 10.6052/0459-1879-17-378

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THE CALIBRATION OF MICRODEFECTS INDUCED EQUIVALENT DAMAGE AREA/VOLUME OF BRITTLE MATERIALS BY USING THE M-INTEGRAL

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China

Received Date: November 13, 2017

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Abstract

Abstract

In view of the integrity, reliability and functionality of brittle materials are substantially limited by the existence of microdefects, the calibration of materials’ damage level is of great scientific value and underlying engineering applications. An unified method of evaluating the microdefects induced equivalent damage area/volume is proposed in present study by the aid of M-integral. The damage area/volume induced by underlying multiple microdefects is assumed as equivalent to the area/volume of an individual circular/spherical void while the values of M-integral are equal for the both cases. Firstly, the analytical expression of M-integral is deduced by using the Lagrangian energy density function, the corresponding physical meaning is briefly elucidated. The domain integral method is applied to numerically calculating the M-integral for both two-dimensional (2D) and three-dimensional (3D) cases. Subsequently, the damage calibration process of arbitrary dispersed microdefects is given, the corresponding equivalent damage area for 2D defects and volume for 3D defects are defined. Finally, the elastic 2D plane and 3D body under uniaxial tensile loading condition is simulated, within which a series of different defect configurations are considered, including the singular defect (void, crack and ellipse) and the dual-defects (void-void, crack-crack, void-crack). Corresponding equivalent damage area or volume are calculated, the inherent “interactive effects” and influence factors are elucidated detailedly and quantitatively. Through the proposed damage calibration method in this study, we can estimate the damage level of any microdefects within brittle solids, the calibration process is simple and convenient, which will be beneficial to the damage tolerance design and integrity assessment of engineering structures.
- microdefects,
- M-integral,
- equivalent damage area,
- equivalent damage volume

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[1]	Shao JF, Rudnicki JW. A microcrack-based continuous damage model for brittle geomaterials. Mechanics of Materials, 2000, 177-180(10): 607-619
[2]	嵇醒. 断裂力学判据的评述. 力学学报, 2016, 48(4): 741-753
[2]	(Ji Xing.A critical review on criteria of fracture mechanics.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 741-753 (in Chinese))
[3]	Chen YH.M-integral analysis for two-dimensional solids with strongly interacting microcracks. Part 1: In an infinite brittle solid.International Journal of Solids and Structures, 2001, 38(18): 3193-3212
[4]	Chen YH.M-integral analysis for two-dimensional solids with strongly interacting microcracks. Part 2: In the brittle phase of an infinite metal/ceramic bimaterial.International Journal of Solids and Structures, 2001, 38(18): 3213-3232
[5]	Ju JW, Chen TM.Effective elastic moduli of two-dimensional brittle solids with interacting microcracks, part II: Evolutionary damage models.Journal of Applied Mechanics, 1994, 61(2): 358-366
[6]	Hu Y, Chen Y.The M -integral description for a brittle plane strip with two holes before and after coalescence.Acta Mechanica, 2009, 204(1-2):109-123
[7]	Yu MH.Advances in strength theories for materials under complex stress state in the 20th Century.Advances in Mechanics, 2004, 34(4): 529-560
[8]	GB/T1979-2001. 结构钢低倍组织缺陷评级图
[8]	(GB/T1979-2001. Standard diagrams for macrostructure and defect of structural steels (in Chinese))
[9]	Pak YE, Mishra D, Yoo SH.Energy release rates for various defects under different loading conditions. Journal of Mechanical Science and Technology, 2012, 26(11): 3549-3554
[10]	徐真军, 杨红兵.关于条形缺陷的射线照相评级探讨.无损探伤, 2010, 34(2): 28-29
[10]	(Xu Zhenjun, Yang Honbing.Analysis of the strip defect rating by using the radiography technology.Nondestructive Testing, 2010, 34(2): 28-29 (in Chinese))
[11]	汪孝欢, 牛显明, 张鹏林等. 焊缝数字图像圆形缺陷的自动评级方法. 无损检测, 2012, 34(9): 42-45
[11]	(Wang Xiaohuan, Niu Xianming, Zhang Penglin, et al.Research on automatic rating method for digital image circular weld defects.Nondestructive Testing, 2012, 34(9): 42-45 (in Chinese))
[12]	Eshelby JD, Frank FC, Nabarro FRN.XLI. The equilibrium of linear arrays of dislocations.Philosophical Magazine, 1951, 42(327): 351-364
[13]	Baxevanakis KP, Giannakopoulos AE.Finite element analysis of discrete edge dislocations: Configurational forces and conserved integrals.International Journal of Solids & Structures, 2015, 62: 52-65
[14]	Judt PO, Ricoeur A.A new application of M- and L-integrals for the numerical loading analysis of two interacting cracks.Journal of Applied Mathematics and Mechanics, 2015, 96(1): 24-36
[15]	Özenç K, Chinaryan G, Kaliske M.A configurational force approach to model the branching phenomenon in dynamic brittle fracture.Engineering Fracture Mechanics, 2016, 157: 26-42
[16]	古斌, 郭宇立, 李群. 基于构型力断裂准则的裂纹与夹杂干涉问题. 力学学报, 2017, 49(6): 1312-1321
[16]	(Gu Bin, Guo Yuli, Li Qun.Crack interacting with an individual inclusion by the fracture criterion of configurational force.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1312-1321 (in Chinese))
[17]	Guo YL, Li Q.Material configurational forces applied to mixed mode crack propagation.Theoretical and Applied Fracture Mechanics, 2017, 89: 145-157
[18]	Tracy J, Waas A, Daly S.Experimental assessment of toughness in ceramic matrix composites using the J -integral with digital image correlation part I: Methodology and validation.Journal of Materials Science, 2015, 50(13): 4646-4658
[19]	Paxevanakis BK, Giannakopoulos AE.Finite element analysis of discrete edge dislocations: Configurational forces and conserved integrals.International Journal of Solids and Structures, 2015, 62(52-65): 52-65
[20]	李群. 材料构型力学及其在复杂缺陷系统中的应用. 力学学报, 2015, 47(2): 197-214
[20]	(Li Qun.Material configurational mechanics with application to complex defects.Acta Mechanica Sinica, 2015, 47(2): 197-214 (in Chinese))
[21]	Hu YF, Chen YH.The M-integral description for a brittle plane strip with two cracks before and after coalescence.Journal of Applied Mechanics, 2009, 76(6): 061017
[22]	于宁宇, 李群. M积分与夹杂/缺陷弹性模量的显式关系. 力学学报, 2014, 46(1): 87-93
[22]	(Yu Ningyu, Li Qun.The explicit relation between the m-integral and the elastic moduli of inclusion/damages.Acta Mechanica Sinica, 2014, 46(1): 87-93 (in Chinese))
[23]	Yu NY, Li Q.Failure theory via the concept of material configurational forces associated with the M-integral.International Journal of Solids & Structures, 2013, 50(25-26): 4320-4332
[24]	Li Q, Guo YL, Hou JL, et al.The M- integral based failure description on elasto-plastic materials with defects under biaxial loading.Mechanics of Materials, 2017, 112: 163-171
[25]	Goldstein RV, Shifrin EI, Shushpannikov PS.Application of invariant integrals to the problems of defect identification.International Journal of Fracture, 2007, 147(1-4): 45-54
[26]	Gommerstadt BY.The J and M integrals for a cylindrical cavity in a time-harmonic wave field.International Journal of Engineering Science, 2014, 83: 76-84
[27]	Meyer CR, Hutchinson JW, Rice JR. The path-independent M integral implies the creep closure of englacial and subglacial channels. Journal of Applied Mechanics, 2016, 84(1):011006(1-9)
[28]	Ma LF, Chen YH, Liu CS.On the relation between the M-integral and the change of the total potential energy in damaged brittle solids.Acta mechanica, 2001, 150(1): 79-85
[29]	Li FZ, Shih CF, Needleman A.A comparison of methods for calculating energy release rates.Engineering Fracture Mechanics, 1985, 21(2): 405-421
[30]	Moran B, Shih CF.A general treatment of crack tip contour integrals.International Journal of Fracture, 1987, 35(4): 295-310
[31]	Nikishkov GP, Atluri SN.An equivalent domain integral method for computing crack-tip integral parameters in non-elastic, thermo-mechanical fracture.Engineering Fracture Mechanics, 1987, 26(6): 851-867
[32]	Shivakumar KN, Raju IS.An equivalent domain integral method for three-dimensional mixed-mode fracture problems.Engineering Fracture Mechanics, 1992, 42(6): 935-959
[33]	Chen YZ, Lee KY.Analysis of the M-integral in plane elasticity.Journal of Applied Mechanics, 2004, 71(4): 572-574
[34]	Seo SY, Mishra D, Park CY, et al.Energy release rates for a misfitted spherical inclusion under far-field mechanical and uniform thermal loads.European Journal of Mechanics, 2015, 49: 169-182

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[8]	ON THE BUECKNER WORK CONJUGATE INTEGRAL AND ITS RELATIONS TO THE J-INTEGRAL AND M-INTEGRAL IN PIEZOELECTRIC MATERIALS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(5): 625-632. DOI: 10.6052/0459-1879-1999-5-1995-074
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