Fracture Behavior of Cement-Based Materials
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Fracture Behavior of Cement-Based Materials S.P. Shah, C. Ouyang, and D.A. Lange
or
(1)
where K, = (EG)m and KK = (ERC)W for the plain stress condition, £ is Young's modulus, and K} is termed the stress intensity factor for mode I crack. Rc or KK is a material constant for brittle materials, and growth of the initial flaw may mean catastrophic failure of the structure. However, R is not constant for quasibrittle materials, and the magnitude of R rises gradually due to the presence of crack arrest mechanisms. Increases of the load as well as the strain energy release rate are accompanied by increased fracture resistance. As a result, the crack steadily propagates until a second condition is also satisfied (see Figure 2):
Introduction The characterization of fracture behavior is a continuing challenge to the cement and concrete community. The performance of a material can be evaluated by its stressstrain response. For an ideally brittle material, elastic response is terminated when stress suddenly drops to zero, as shown in Figure la. However, cement-based materials are considered quasi-brittle because they respond nonlinearly prior to peak stress, and their stress gradually decreases after reaching a peak, as indicated in Figure lb. To make cement-based materials stronger and tougher, one needs to understand the fracture mechanisms associated with nonlinear stress-strain behavior and to characterize material fracture properties based on these fracture mechanisms. Three novel techniques are being used at the Center for Advanced Cement-Based Materials (ACBM) to detect the quasi-brittle nature of cementbased materials. These three techniques are laser holographic interferometry, acoustic emission, and microscopic surface analysis. This article summarizes both the fracture mechanisms in cement-based materials and the application of the three techniques to characterize and measure fracture properties.
da
Strain (a) Brittle material
Strain (b) Quasi-brittle material
Figure 1. Stress-strain curves for different materials: (a) Brittle material, and (b) quasi-brittle material.
Critical point: Macroscopic Characteristics of Quasi-brittle R =G Quasi-Brittle Materials dG dB Fracture properties of quasi-brittle mada - da terials can be described by a fracture resiso d: tance curve (R-curve). When a material G-curve with an inherent flaw (a0) is loaded, the R-curve potential energy (ii) changes due to possible extension (da) of the flaw at the rate Brittle materials dll/da = G (the strain energy release rate). (LEFM) On the other hand, crack extension at the crack tip needs to consume some energy, which is denoted as W at the rate dW/da = R Crack Length (the fracture resistance). Consequently, the linear elastic fracture mechanics (LEFM) criterion for extension of a two-dimensional Figure 2. R-curve for quasi-brittle mode I crack is: materials.
MRS BULLETIN/MARCH 1993
materials
da
(2)
The crack length that simultaneously satisfies conditions (1) and (2) is the critical crack length and is denoted as acMany crack-arr
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