# Cracking and Fracture in Concrete

## Development of Microcracking

The non-linear stress–strain behaviour of concrete in compression is largely due to the increasing contribution of microcracking to the strain with increasing load. Four stages of cracking behaviour have been identified (Glucklich, 1965):

**Stage 1**, up to about 30% maximum stress. The pre-existing transition-zone cracks remain stable, and the stress–strain curve remains approximately linear.**Stage 2**, about 30 – 50% maximum stress. The cracks begin to increase in length, width and number, causing non-linearity, but are still stable and confined to the transition zone.**Stage 3**, about 50 – 75% maximum stress. The cracks start to spread into the matrix and become unstable, resulting in further deviation from linearity.**Stage 4**, above about 75% ultimate stress. Spontaneous and unstable crack growth becomes increasingly frequent, leading to very high strains. Also at this stage the excessive cracking results in the lateral strains increasing at a faster rate than the axial strains, resulting in an overall increase in volume (Fig. 1).

Complete breakdown, however, does not occur until strains significantly higher than those at maximum load are reached. Fig. 2 shows stress– strain curves from strain-controlled tests on paste, mortar and concrete. The curve for HCP has a small descending branch after maximum stress; with the mortar it is more distinct, but with the concrete it is very lengthy.

During the descending region, excess cracking and slip at the paste–aggregate interface occur before the cracking through the HCP is sufficiently well developed to cause complete failure.

## Creep Rupture

The contribution of microcracking to creep increases with stress level to the extent that if a stress sufficiently close to the short-term ultimate is maintained then failure will eventually occur, a process known as creep rupture. There is often an acceleration in creep rate shortly before rupture. The behaviour can be shown by stress–strain relationships plotted at successive times after loading, giving an ultimate strain envelope, as shown for compressive and tensile loading in Fig. 3a and Fig. 3b, respectively.

The limiting stress below which creep rupture will not occur is about 70% of the short-term maximum for both compression and tension.

## The Fracture Mechanics Approach

Griffith’s theory for the fracture of materials and its consequent development into fracture mechanics were described in general terms.

Not surprisingly, there have been a number of studies attempting to apply linear fracture mechanics to concrete, with variable results; some of the difficulties encountered have been:

- Failure in compression, and to a lesser extent in tension, is controlled by the interaction of many cracks, rather than by the propagation of a single crack.
- Cracks in cement paste or concrete do not propagate in straight lines, but follow tortuous paths around cement grains, aggregate particles etc., which both distort and blunt the cracks.
- The measured values of fracture toughness are heavily dependent on the size of the test specimen, and so could not strictly be considered as a fundamental material property.
- Concrete is a composite made up of cement paste, the transition zone and the aggregate, and each has its own fracture toughness (K
_{c}), each of which is difficult to measure.

Despite these difficulties, K_{c} values for cement paste have been estimated as lying in the range 0.1 to 0.5 MN/m^{3/2}, and for concrete between about 0.45 and 1.40 MN/m^{3/2} (Mindess and Young, 1981). K_{c} for the transition zone seems to be smaller, about 0.1 MN/m^{3/2}, confirming the critical nature of this zone.

## Strength Under Multiaxial Loading

So far in our discussions on compressive strength have been concerned with the effects of uniaxial loading, i.e. where σ_{1} (or σ_{x}) is finite, and the orthogonal stresses σ_{2} (or σ_{y}) and σ_{3 }(or σ_{z}) are both zero.

In many, perhaps most, structural situations concrete will be subject to a multiaxial stress state (i.e. σ_{2} and/or σ_{3 }as well as σ_{1} are finite). This can result in considerable modifications to the failure stresses, primarily by influencing the cracking pattern.

A typical failure envelope under biaxial stress (i.e. σ_{3} = 0) is shown in Fig. 4, in which the applied stresses, σ_{1} and σ_{2}, are plotted non-dimensionally as proportions of the uniaxial compressive strength, σc.

Firstly, it can be seen that concretes of different strengths behave very similarly when plotted on this basis. Not surprisingly, the lowest strengths in each case are obtained in the tension–tension quadrant.

The effect of combined tension and compression is to reduce considerably the compressive stress needed for failure even if the tensile stress is significantly less than the uniaxial tensile strength.

The cracking pattern over most of this region (Type 1 in Fig. 4) is a single tensile crack, indicating that the failure criterion is one of maximum tensile strain, with the tensile stress enhancing the lateral tensile strain from the compressive stress.

In the region of near uniaxial compressive stress, i.e. close to the compressive stress axes, the cracking pattern (Type 2) is essentially the same as that in the central region of the cylinder i.e. the cracks form all around the specimen approximately parallel to the compressive load.

In the compression–compression quadrant, the cracking pattern (Type 3) becomes more regular, with the cracks forming in the plane of the applied loads, splitting the specimen into slabs. Under equal biaxial compressive stresses, the failure stress is somewhat larger than the uniaxial strength. Both Type 2 and Type 3 crack patterns also indicate a limiting tensile strain failure criterion, in the direction perpendicular to the compressive stress(es).

With triaxial stresses, if all three stresses are compressive then the lateral stresses (σ_{2} and σ_{3}) act in opposition to the lateral tensile strain produced by σ_{1}. This in effect confines the specimen, and results in increased values of σ_{1} being required for failure, as illustrated in Fig. 5 for the case of uniform confining stress (i.e. σ_{2} = σ_{3}); the axial strength (σ_{1ult}) can be related to the lateral stress by the expression:

σ_{1ult} = σ_{c} + Kσ_{2} (or σ_{3})

where K has been found to vary between about 2 and 4.5.

When a compressive stress is applied to a specimen by the steel platen of a test machine, the lateral (Poisson effect) strains induce restraint forces in the concrete near the platen owing to the mismatch in elastic modulus between the concrete and the steel. This is therefore a particular case of triaxial stress, and the cause of the higher strength of cubes compared to longer specimens such as cylinders.

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