For several decades it has been clear that the size effect on structural strength, exhibiting a major non-statistical component, is a quintessential property of all quasibrittle materials. However, progress in design codes and practice for these materials has been retarded by protracted controversies about the proper mathematical form and justification of the size effect law (SEL). A fresh exception is the American Concrete Institute which, in 2019, becomes the first concrete code-making society to adopt the SEL based on quasibrittle fracture mechanics. This article begins by discussing several long-running controversies that have recently abated, and then focuses critically on the so-called Boundary Effect Model (BEM), promoted for concrete relentlessly for two decades, in ever-changing versions, by Xiaozhi Hu et al. The BEM is here compared to the quasibrittle SEL based on asymptotic matching. Its errors, weaknesses and inconsistencies are identified—including incorrect large- and small-size asymptotic size effects, conflicts with broad-range comprehensive test data and with the cohesive crack model, incorrect aggregate-size dependence of strength, illogical dependence on ligament stress profile, inability to capture the statistical part of size effect at large sizes, simplistic effect of boundary proximity, and lack of distinction between Type 1 and 2 size effects. In contrast to the SEL, the BEM is not applicable to mixed and shear fracture modes and to complex geometries of engineering structures, and is not transplantable from concrete to other quasibrittle materials. The purpose of this critique is to help crystallize a consensus about the proper size effect formulation, not only for concrete structures but also, and mainly, for other quasibrittle materials and structures, including airframes made of fiber composites, ceramic components and micrometer-scale devices, and for failure assessments of sea ice, rock, stiff soils, bone, and various bio- or bio-mimetic materials, for all of which the non-statistical size effect is yet to be widely accepted in practice.
Bibliographical noteFunding Information:
CC would like to acknowledge the start up fund provided by Case Western Reserve University , which was partially used to support this research. MS acknowledges the financial support from the Haythornthwaite Foundation through the ASME Haythornthwaite Young Investigator Award. JL thanks NSF for partial support under grant CMMI- 1361868 to the University of Minnesota. CGH thanks Arizona State University and the Ira A. Fulton Schools of Engineering for providing research startup funds to conduct this research. ZPB thanks ARO for partial support under grant W911NF-19-1-0039 to Northwestern University. Discussions in ACI Committee 446, Fracture Mechanics, under the current chair CC and past chair CG, were particularly helpful.
- Analysis of experimental data
- Concrete structures
- Design codes
- Energetic size effect
- Fracture mechanics
- Quasibrittle materials
- Size effect justification
- Size effect law
- Statistical size effect