On the ductile enlargement of voids in triaxial stress fields

TLDR: In this article, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material.

Abstract: The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. First, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and subjected to a remotely uniform stress and strain rate field. Then an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material. Growth is studied in some detail for the case of a remote tensile extension field with superposed hydrostatic stresses. The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. Some related results are discussed, including the long cylindrical void considered by F.A. McClintock (1968, J. appl. Mech . 35 , 363), and an approximate relation is given to describe growth of a spherical void in a general remote field. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "On the ductile enlargement of voids in triaxial stress fiet,ds*" ?

Growth is studied in some detail for the ease of a remote tensile estensioo field with superposed hydrostatic stresses. Some related results are discussed, including the long cylindrical void considered by F. A. MCCLINTOCK ( 1968, J. uppl. Mech. 35, 363 ), and an approsimate relation is given to describe growth of a spherical void in a general remote field. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension. 

Q2. What is the void growth rate in a remote field?

The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. 

Q3. What is the void growth in a ductile solid?

Rogers explains that the central portion of the CLIP and cone fracture which occurs at the neck of a specimen is produced by the coalescence of internal voids which grow by plastic deformation under the influence of the prevailing triaxial stress system. 

Q4. What is the boundary condition for a viscous material?

F4 (R) sinndtnneously satisfies both the bonded inclusion and zero shear strain rate boundary conditions, and t,hcreforc cannot be a viscous solution. 

Q5. What is the procedure for examining the bonndar conditions?

Of course, the best procedure would bc to let the variational principle serve as a basis for choice of F (II’) through the associated Euler-Lagrange differential CY~LGI tion, rather than to examine a set of different choices with ord>~ the multiplying factor E as a free paramctcr. 

Q6. What is the corresponding two-dimensional version of the functional Q (ti) in our?

The corresponding two-dimensional version of the functional Q (ti) in their general development iswhcrc i is tire strain rate dcrix-cd from the \\-elocity field (46). 

Q7. What is the ductile enlargcrucut of voids?

On the ductile enlargcrucut of voids iu triaxial strcas: ficl~ls___----- _._.-for F.+(R)__/-d The authoraveraae l+E for F.(R) to F.(R) ------ ------for F,(R) ________-,;=-=-z-rrl___ --for F,(R) \\for F,(R)‘tooFIG.