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The Overview of Fracture Mechanics Models for Concrete

Amanda AKRAM
Amanda AKRAM
   | 17. Apr. 2021
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Online veröffentlicht: 17. Apr. 2021
Seitenbereich: 47 - 57
Eingereicht: 24. Sept. 2020
Akzeptiert: 22. Feb. 2021
DOI: https://doi.org/10.21307/acee-2021-005
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© 2019 Amanda Akram published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Illustration of fracture parameters: a descending branch of stress-displacement curve (a) and a generalized bilinear softening function (b)
Illustration of fracture parameters: a descending branch of stress-displacement curve (a) and a generalized bilinear softening function (b)

Figure 2.

The strain-softening phenomenon in the post-peak range and the fictitious crack model for concrete in tension [9]
The strain-softening phenomenon in the post-peak range and the fictitious crack model for concrete in tension [9]

Figure 3.

The visualization of the crack morphology (a), the model of strain distribution in the fracture process zone and its vicinity (b), the crack band model (CBM) concept with the crack band width wc (c) and the fictitious crack model (FCM) concept for comparison (d)
The visualization of the crack morphology (a), the model of strain distribution in the fracture process zone and its vicinity (b), the crack band model (CBM) concept with the crack band width wc (c) and the fictitious crack model (FCM) concept for comparison (d)

Figure 4.

A notched beam in a three-point bending test with parameters of Jenq – Shah model
A notched beam in a three-point bending test with parameters of Jenq – Shah model

Figure 5.

Theoretical basics of modified two parameter fracture model: the deflection (kinking) angle θ, effective critical crack length ae, a1 and a2 together form the kinked crack branch [27]
Theoretical basics of modified two parameter fracture model: the deflection (kinking) angle θ, effective critical crack length ae, a1 and a2 together form the kinked crack branch [27]

Figure 6.

An example of a P – CMOD curve for the purposes of calculating the double – K fracture parameters, where: Cu – the unloading compliance, Pini – initial cracking load, CMODp – plastic crack mouth opening, CMODe – elastic crack mouth opening. From point 0 to 1 the fracture process can be characterized as elastic and there is no further propagation of the initial crack, at point 2 maximum load Pmax is achieved
An example of a P – CMOD curve for the purposes of calculating the double – K fracture parameters, where: Cu – the unloading compliance, Pini – initial cracking load, CMODp – plastic crack mouth opening, CMODe – elastic crack mouth opening. From point 0 to 1 the fracture process can be characterized as elastic and there is no further propagation of the initial crack, at point 2 maximum load Pmax is achieved

Figure 7.

The cohesive stress distribution σ(x) in the fictitious crack zone at the peak load; ao – initial crack length, ac – critical crack length, ft – tensile strength of concrete
The cohesive stress distribution σ(x) in the fictitious crack zone at the peak load; ao – initial crack length, ac – critical crack length, ft – tensile strength of concrete

Figure 8.

Size effects for geometrically similar structures on a bi-logarithmic scale with strength criterion and LEFM asymptotes (dashed lines). Solid arched line shows the transitional behavior of concrete between different types of size effects [37]
Size effects for geometrically similar structures on a bi-logarithmic scale with strength criterion and LEFM asymptotes (dashed lines). Solid arched line shows the transitional behavior of concrete between different types of size effects [37]

Figure 9.

The effects of multiscaling fractal law on a bi-logarithmic scale: a) for the fracture energy, b) for the tensile stress; b – the characteristic reference size, dG – the fractional increment of the energy dissipation, dσ – the fractional decrement caused by the analyzed disorder
The effects of multiscaling fractal law on a bi-logarithmic scale: a) for the fracture energy, b) for the tensile stress; b – the characteristic reference size, dG – the fractional increment of the energy dissipation, dσ – the fractional decrement caused by the analyzed disorder

Figure 10.

The member boundary – crack tip relation in the boundary effect concept: a) the case of a “short crack”, when the crack’s tip is close to the edge, in other words front boundary, b) the crack tip is remote from both front and back boundaries and the linear elasticity’s rules applies, c) the case of a “short ligament” when the crack tip is close to the back boundary. The hatched area corresponds to the fracture process zone
The member boundary – crack tip relation in the boundary effect concept: a) the case of a “short crack”, when the crack’s tip is close to the edge, in other words front boundary, b) the crack tip is remote from both front and back boundaries and the linear elasticity’s rules applies, c) the case of a “short ligament” when the crack tip is close to the back boundary. The hatched area corresponds to the fracture process zone
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