Significance Of Stress Intensity Factor On Failure Behaviour Of Reinforced Concrete Beam (A case study of: Mode I Fracture)

The term Stress Intensity Factor – SIF, is one of the fracture parameters which describes stress intensity around crack tip, represented by variable K. Depends on its critical value Kc, structural failure capacity might be analyzed based on the view of point of fracture mechanics. This study focuses on how reinforcement influences the rate of crack propagation. Wedge forces developed by cohesiveness between re-bar and concrete is the main concern in transforming brittle failure to plastic failure by means reducing the value of K. Specimen with three point mode I fracture reinforced high strength concrete beam was used in analytical processing. It is a mode I fracture beam of (150x300) mm with 100 mm initial crack. This specimen is reinforced by 4#12mm steel bar. Under wedge forces due to a center bending load, led a value of K equal to 482.70 Nmm for beam without reinforcement, whereas 441.613 Nmm for beam with reinforcement.Superposition of these both actions prevails the net of stress intensity factor K = 41.087Nmm. By applying the term strain energy released rate G in conjunction with stress intensity factor K through the relationship K = EG, prevails, netto of G = 35 N/m , a value under which normal plain concrete would fail. -------------------------------------------------------------------------------------------------------------------------------------Date of Submission: 07-05-2018 Date of acceptance: 22-05-2018 -------------------------------------------------------------------------------------------------------------------------------------I. Background Concrete structures are full of cracks [1] . This phenomenon comes from initial internal discontinuity which occurs due to some reasons, such as imperfection during the mixing of constituent component of concrete material. Internal cracks, have the potential to increase the stress intensity factor, K, around the cracktip. K is known as fracture toughness supplied by energy absorption due to external loads. The magnitude of K is significantly influenced by the crack tip geometry and external load configuration. Fig 1. Transition of brittle to ductile failure From the standpoint of concrete fracture mechanics, the accumulated stress intensity at the crack tip should be limited such that, under the increment of loading, stable growth of large fracture process zone (FPZ) would be in charge before the ultimate load is reached. This is what the concept of ductility underlies especially in earthquake resistant structures. By adding reinforcement, Reinforcement is a driving force that generates composite action between re-bars and concrete, hence, it is able to divert the brittle failure gradually to quasibrittle, and finally to ductile, as shown in Fig.1 Significance Of Stress Intensity Factor On Failure Behaviour Of Reinforced Concrete Beam www.ijesi. org 69 | Page II. Literature Review 2.1 Stress Intensity Factor The stress intensity factor K was developed in 1957 by Irwin [5] , defines the magnitude of the local stresses around the crack tip. Please note that this factor depends on loading, crack size, crack shape, and geometric boundaries, with the general form given by K = σ πa. for infinite structure 1 K = σ πa g1 a b . for finite structures 2 In case of bending (shown by Fig.2), eq.2 is applied where a is the length of initial crack, b and t are the beam dimensions, and g1 is the geometry function, calculated as g1 a b = 1.0−2.5 a⁄b+4.49(a⁄b)2−3.98(a⁄b)3+1.33(a⁄b)4 1−a b 3 2 3 The term stress σ is the stress due to P, acts perpendicular the crack face, counted as σ = 1.5PS 2td2 4 On the concept of strength state design, capacity of structure is modeled on the internal forces equilibrium (concrete compressive and steel tensile). For bending the following equation must be met, Mnf = Mu 5 where Mnf is nominal moment which must be greater at least equal to the ultimate external moment. That postulation might be expressed by the compatibility between the energy absorbed when loading and energy released when unloading. Please be noticed that in case of cracks, unloading occurs simultaneously with crack propagation for quasi brittle materials (analog with yielding for ductile materials). Griffith (1920) [4] proposed the concept of strain energy release rate to demonstrate the equilibrium states of a structure with a crack as Π = U − F + W 6 where Π is the total potential energy, U is the strain energy, F is the work done by the applied force, and W is the energy for crack formation. The necessary condition for the structure in equilibrium states is that the first order derivative of П is equal to zero during an infinitesimal crack extension da, that is ∂ ∂a U − F + W = 0 7