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Research Papers

Cohesive Zone-Based Damage Evolution in Periodic Materials Via Finite-Volume Homogenization

[+] Author and Article Information
Wenqiong Tu

Civil Engineering Department,
University of Virginia,
Charlottesville, VA 22904-4742

Marek-Jerzy Pindera

Mem. ASME
Civil Engineering Department,
University of Virginia,
Charlottesville, VA 22904-4742

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 29, 2014; final manuscript received July 26, 2014; accepted manuscript posted August 13, 2014; published online August 13, 2014. Assoc. Editor: Nick Aravas.

J. Appl. Mech 81(10), 101005 (Aug 13, 2014) (16 pages) Paper No: JAM-14-1141; doi: 10.1115/1.4028103 History: Received March 29, 2014; Revised July 26, 2014; Accepted July 30, 2014

The zeroth-order parametric finite-volume direct averaging micromechanics (FVDAM) theory is further extended in order to model the evolution of damage in periodic heterogeneous materials. Toward this end, displacement discontinuity functions are introduced into the formulation, which may represent cracks or traction-interfacial separation laws within a unified framework. The cohesive zone model (CZM) is then implemented to simulate progressive separation of adjacent phases or subdomains. The new capability is verified in the linear region upon comparison with an exact elasticity solution for an inclusion surrounded by a linear interface of zero thickness in an infinite matrix that obeys the same law as CZM before the onset of degradation. The extended theory's utility is then demonstrated by revisiting the classical fiber/matrix debonding phenomenon observed in SiC/Ti composites, illustrating its ability to accurately capture the mechanics of progressive interfacial degradation.

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Figures

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Fig. 1

A reference square subvolume in the η–ξ plane (left) mapped onto a quadrilateral subvolume in the y2y3 plane (right) of the actual microstructure

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Fig. 2

Interfacial discontinuity between two adjacent subvolumes

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Fig. 3

Traction-interfacial separation relations for the CZM in normal (left column) and tangential (right column) directions to the interface: graphical representations of (a) coupled and (b) uncoupled relations

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Fig. 4

Unit cell geometry containing 0.05 fiber volume fraction (left) and a detailed close-up (right) used for comparison with the Eshelby solution for an inclusion with a linear interface in an infinite matrix

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Fig. 5

Comparison of radial and tangential displacement discontinuities around the fiber/matrix interface obtained from modified Eshelby and dilute FVDAM solutions

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Fig. 6

Comparison of normal and tangential stress fields in the region occupied by the unit cell obtained from modified Eshelby and dilute FVDAM solutions based on the interfacial properties in Table 1

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Fig. 7

Comparison of normal and tangential stress fields in the region occupied by the unit cell obtained from modified Eshelby and dilute FVDAM solutions with the interfacial properties set to simulate the Kirsch solution

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Fig. 8

Initial transverse response of the unidirectional SiC/Ti composite with different interfacial strengths, illustrating the effect of fabrication-induced residual stresses

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Fig. 9

Comparison of the applied (vertical axis) and calculated (horizontal axis) homogenized strains based on Eq. (33), demonstrating consistency and accuracy of the implemented solution technique for the nonlinear response of the unit cell based on the implemented CZM, and importance of the contributions of the interfacial displacement discontinuities toward total homogenized strains

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Fig. 10

Initial transverse response of the unidirectional SiC/Ti composite immediately after fabrication cooldown, illustrating the effect of (a) uncoupled and (b) coupled interfacial separation laws

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Fig. 11

Interfacial displacement discontinuity and traction distributions around the fiber/matrix interface with progressively greater applied load after fabrication cooldown

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Fig. 12

Full-field stress distributions at progressively greater applied load after fabrication cooldown

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Fig. 13

Transverse response of the representative unit cell of unidirectional SiC/Ti composite with different interfacial debonding lengths after initial preloading

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Fig. 14

Interfacial displacement discontinuity and traction distributions around the fiber/matrix interface with progressively greater applied load after initial preloading

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Fig. 15

Full-field stress distributions at progressively greater applied load after fiber/matrix degradation by initial preloading

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