TY - JOUR

T1 - Stable growth of fracture in brittle aggregate materials

AU - Wnuk, Michael P.

AU - Bažant, Zdeněk P.

AU - Law, Edward

N1 - Funding Information:
The work was sponsored under U.S. National Science Foundation Grant No. CEE800-9050 to Northwestern University, directed by Z.P. Ba~ant. M.P. Wnuk, Visiting Professor at Northwestern University, and Edward Law appreciate financial support under this grant. Mary Hill is to be thanked for her excellent secretarial assistance.

PY - 1984/12

Y1 - 1984/12

N2 - Fracture of concrete is analyzed by combining the resistance curve (R-curve) approach with linearly elastic solutions for the energy release rate resulting from the quasi-static crack model of Wnuk, analogous to the D-BCS model of a stationary crack used in describing quasi-brittle fracture in metals. The R-curve, representing the crack length dependence of the energy consumed per unit fracture extension, is calculated using the concept of the energy separation rate associated with a finite crack growth steps. To simplify calculations, the tensile stress transmitted across the nonlinear zone ahead of the fracture front is assumed to be uniformly distributed over the entire nonlinear zone, even though in reality it must be a gradually declining stress resulting in strain-softening; and an infinite elastic medium loaded at infinity is assumed. These assumptions permit an easy solution with the help of Green's function for an infinite elastic medium. Application to bodies of finite size then requires assuming the nonlinear zone (fracture process zone) to be negligible with regard to specimen dimensions, crack length and ligament length. Even though this assumption is not always realistic, the end results, which are of practical importance, appear reasonable. The analysis leads to a nonlinear first-order ordinary differential equation for the R-curve, which is integrated numerically. The R-curves calculated in this manner can be closely fitted to data from previous fracture tests. Only two parameters, characterizing the initial and the final lengths of the nonlinear zone, need to be adjusted to test data.

AB - Fracture of concrete is analyzed by combining the resistance curve (R-curve) approach with linearly elastic solutions for the energy release rate resulting from the quasi-static crack model of Wnuk, analogous to the D-BCS model of a stationary crack used in describing quasi-brittle fracture in metals. The R-curve, representing the crack length dependence of the energy consumed per unit fracture extension, is calculated using the concept of the energy separation rate associated with a finite crack growth steps. To simplify calculations, the tensile stress transmitted across the nonlinear zone ahead of the fracture front is assumed to be uniformly distributed over the entire nonlinear zone, even though in reality it must be a gradually declining stress resulting in strain-softening; and an infinite elastic medium loaded at infinity is assumed. These assumptions permit an easy solution with the help of Green's function for an infinite elastic medium. Application to bodies of finite size then requires assuming the nonlinear zone (fracture process zone) to be negligible with regard to specimen dimensions, crack length and ligament length. Even though this assumption is not always realistic, the end results, which are of practical importance, appear reasonable. The analysis leads to a nonlinear first-order ordinary differential equation for the R-curve, which is integrated numerically. The R-curves calculated in this manner can be closely fitted to data from previous fracture tests. Only two parameters, characterizing the initial and the final lengths of the nonlinear zone, need to be adjusted to test data.

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U2 - 10.1016/0167-8442(84)90032-6

DO - 10.1016/0167-8442(84)90032-6

M3 - Article

AN - SCOPUS:3242798242

VL - 2

SP - 259

EP - 286

JO - Theoretical and Applied Fracture Mechanics

JF - Theoretical and Applied Fracture Mechanics

SN - 0167-8442

IS - 3

ER -