یک مدل انتشار ترک بهبود یافته برای بتن ساده تحت بار خستگی An improved crack propagation model for plain concrete under fatigue loading

1. Introduction Fatigue phenomenon is prevalent in various concrete structures namely, airport runways, railway bridges, highway pavements, offshore structures, etc. during the service period. Existence of pre-existing flaws triggers the initiation of cracks when subjected to repetitive load cycles and leads subsequently to a sizeable crack, ultimately causing the final fracture. Concrete is a quasi-brittle material and contains a large size inelastic zone called fracture process zone ahead of the crack tip. The formation of fracture process zone (FPZ) in concrete is highly complicated due to the inherent heterogeneous nature. This inelastic zone controls the propagation of cracks in concrete considerably in addition to the other material and geometrical parameters. Such a material behaviour has posed a challenge for the accurate prediction of fatigue life and crack growth rate in concrete. One of the earliest fracture mechanics based fatigue crack propagation model defining variation of crack growth rate with respect to change in stress intensity factor has been developed by Paris and Erdogan [1]. Paris law can accurately predict the crack propagation behaviour in metallic structures. The existence of large size FPZ restricts the direct application of Paris law on concrete. In where f u denotes the tensile strength, β = ,d d d0 is specimen depth, d0 has a meaning of transitional size (dimension) of structure. The applicability of above size adjusted Paris law to high strength concrete has been investigated by Bazant and Schell [3] by performing experiments on high strength concrete. Further, it has been recommended that the size adjusted Paris law developed for plain concrete can also be applied for high strength concrete provided the specimen sizes do not vary significantly. Slowik et al. [4] have proposed a fracture mechanics based crack propagation model for plain concrete member under the action of variable amplitude repetitive loading. The effect of load spike applied in between the constant load cycles has been studied by performing experiments on wedge splitting test specimens. Sain and Chandra Kishen [5] have proposed an advanced fatigue crack propagation model for plain and reinforced concrete beam by modifying the model proposed by Slowik et al.[4]. This model incorporates the effect of loading frequency of applied load, loading history and the size effect parameters.