Journal of Rehabilitation in Civil Engineering 6-2 (2018) 29-42 journal homepage: http://civiljournal.semnan.ac.ir/ Ultra-Low Cycle Fatigue Fracture Life of a Type of Buckling Restrained Brace N. Hoveidae* *Assistant Professor, Civil Engineering department, Azarbaijan Shahid Madani University, Tabriz, Iran Corresponding author: [email protected] ARTICLE INFO ABSTRACT Article history: Received: 05 May 2017 Buckling restrained braced frames (BRBFs) are considered as Accepted: 05 September 2017 popular seismic-resistant structural systems. A BRB sustains large plastic deformations without brace buckling. The core of a Keywords: buckling restrained brace is prone to fatigue fracture under cyclic Buckling Restrained Brace, loading. The earthquake induced fracture type of the core plate in a Ultra-Low Cycle Fatigue, buckling restrained brace can be categorized as ultra-low cycle Cyclic Void Growth Model, fatigue fracture. This paper investigates the ultra-low cycle fatigue Finite Element Analysis. fracture life of a type of composite buckling restrained brace previously tested. The newly developed cyclic void growth model was adopted to theoretically predict the fracture and crack initiation in the core. In addition, the Coffin-Manson fatigue damage model was applied to estimate the fracture life of the brace. A FEM model of the BRB developed in ABAQUS was used to evaluate the fatigue life. The analysis results showed that the cyclic void growth model is capable to nearly predict the fracture life of the core in buckling restrained brace. [2], Qiang [3], Watanebe et al. [4], 1. Introduction Tremblay et al. [5], Usami et al. [6,7], Hoveidae et al. [8-10], Chou et al. [11], Recently, Buckling Restrained Braced Eryasar et al. [12]. Fig. 1 illustrates the Frames (BRBFs) are considered as popular typical BRB detail. The encasing member seismic-resisting structural systems. A in a BRB inhibits the brace global buckling BRBF is distinguished from ordinary and minimizes the core local buckling. buckling type brace, where the its buckling A variety of arrangements have been is inhibited by a restraining member. There proposed for BRBs. Hoveidae et al. [10] are different details for BRBs including proposed a novel all-steel BRB in which a all-steel and composite BRBs. The cyclic shorter core plate was used and then the response of a BRB is more stable. BRBs seismic response of SCBRB was evaluated are famous for their higher ductility through nonlinear time history and finite capacity. The ductility in a BRB is element analyses. Bazzaz et al. [13] produced by plastic deformation of core proposed a new type of non-buckling steel member without significant local and ring dissipater in off-center and centric global buckling of the brace. Many bracing systems in order to enhance the researches have been conducted on seismic ductility of braced system. Moreover, response of BRBs which can be found in Bazzaz et al. [14] investigated the behavior the works by Black et al. [1], Inou et al. DOI: 10.22075/JRCE.2017.11262.1185 N. Hoveidae/ Journal of Rehabilitation in Civil Engineering 6-2 (2018) 29-42 30 of off-center bracing system with ductile factor of 8.68 was achieved. Furthermore, element. Andalib et al. [15] analytically Bazzaz et al. [16] proposed a new bracing and experimentally studied the usage of system using circular element (circular steel rings made of steel pipes as an energy dissipater). The analytical results and dissipater at the intersection of braces. comparison between plots of these two These studies showed that the brace with models showed that the first model has the steel ring exhibits a steady and wide higher performance than the others. hysteresis curve and a tensile ductility Fig. 1. Typical configuration of a BRB Ozcelik et al. [17] investigated the buckling-restrained brace to develop the response of BRBs with different types of high-performance BRB used in bridge restraining members. It was found that the engineering were conducted. According to energy dissipation capacity of BRBs the mentioned experimental results, the considerably depends on compression BRBs with stoppers possess a higher low- strength adjustment factor, β, and strain cycle fatigue performance than those hardening adjustment factor, ω. without stoppers. Razavi et al. [18] proposed reduced length Yan-Lin et al. [20] proposed core-separated buckling restrained brace (RLBRB), in BRBs and theoretically and experimentally which a shorter core was sandwiched investigated the behavior of the brace. It between a restraining member. The test was found that the proposed detail results indicated that the reduction in BRB improves flexural rigidity of the restraining core length and consequently the increase system. in strain of core up to amplitudes of 4-5% Most of research areas in the literature enhance the risk of low-cycle fatigue focuses on seismic response of BRBs and failure. The low cycle fatigue response of the lack of studies on low cycle fatigue the core plate was examined by Coffin- response of BRBs is evident. Manson fatigue damage criteria as well. Wang et al. [19] surveyed the low cycle Typically, a core plate in a BRB is made fatigue behavior of all-steel buckling up of a ductile steel rectangular plate. The restrained braces. Experimental and core plate is normally designed according numerical studies on the effect of stoppers to code-based forces. In general, the limit on the low-cycle fatigue performance of state of a BRB is the core fracture at mid- 31 N. Hoveidae/ Journal of Rehabilitation in Civil Engineering 6-2 (2018) 29-42 length or at the core ends close to well-known Coffin–Manson approach transition zones, depending on core details. (Pereira et al. [21]). If a stopper is provided on the core plate to prevent the slippage of restraining Kanvinde and Deierlein [31] proposed member, the core plate tensile fracture is another micro-mechanical based ULCF likely to take place at a region near to the model based on the cyclic behavior of stopper [11]. However, in some cases, micro-voids, which enters the stress especially for the BRBs without stopper, triaxiality effects into material degradation. the fracture tends to attend the core ends The model was called Cyclic Void Growth [18]. The fracture of the core plate in a Model (CVGM). Based on this model, BRB can be classified as a low cycle void growth and shrinkage lead to ductile fatigue or ultra-low cycle fatigue fracture fracture initiation during cyclic loading of problem, depending on the loading history the material. This model was verified for applied. several steel types, geometries and loading histories. Despite the low cycle fatigue Normally, the fracture of steel material response of BRBs is investigated in some under extreme loads occurs at small prior works, which can be found in the number of cycles (less than 100 cycles). literature, the ultra-low cycle fatigue This fatigue regime is called ultra-low response is not deliberated meticulously. In cycle fatigue (ULCF) [21]. The steel this paper, the CVGM is applied to a BRB damage induced by earthquake can be previously tested by Chou et al. [11] in classified as ultra-low cycle fatigue order to predict the ultra-low cycle fatigue (Shimada et al. [22], Kuroda [23], Nip et life. In addition, the fracture life of the core al. [24]), which is categorized by large plate is examined by the well-known plastic strains and few cycles to fracture Coffin-Manson damage rule and compared (Zhou et al. [25]). The ULCF fracture is with that evaluated by CVGM model. often the governing limit state in steel structures subjected to severe earthquakes. 2. CVGM Formulation The extremely random loading histories of ULCF associated with very few cycles Based on the researches by Kanvinde and make them difficult to adapt to techniques Deierlein [31], the two key procedures to developed for high and low cycle fatigue, capture in ULCF regime are void growth such as rain-flow cycle counting method “demand,” including the effects of void (Downing et al. [26]) and strain-life growth and shrinkage/collapse, and approaches proposed by Manson [27] and degraded void growth “capacity,” related Coffin [28]. to cyclic strain concentrations of the inter void ligament material. The CVGM model A number of fatigue damage models, proposed by Kanvinde and Deierlein proposed by various authors are available improves the concepts described by Rice in the literature. ULCF prediction models and Tracey [32], Hancock and Mackenzie are usually categorized into two coupled [33] for monotonic loading, and Ristinmaa and uncoupled models. An example of [34] and Skallerud and Zhang [35] for coupled plasticity-damage models was cyclic loading. The fundamental proposed by Lemaitre [29]. An exponential mechanisms of low cycle fatigue fracture ULCF damage rule was proposed by Xue involve cyclic void growth, collapse, and [30] which is more accurate for life distortion. Fig. 2 represents the ductile prediction in ULCF regime, compared to fracture mechanism in metals based on N. Hoveidae/ Journal of Rehabilitation in Civil Engineering 6-2 (2018) 29-42 32 CVGM model. In addition, a fractograph of ULCF is displayed in Fig. 3 [36]. Fig. 2. Micromechanism of ULCF Fig.3. Fractograph of ULCF First, this paper aims to briefly review the In order to show the fracture through a components of CVGM model. The void void growth index, the calculations above growth rate can be designated by the next can be simplified. equation for a single spherical void, (Rice (VGI ), which is compared to its and Tracey, [32]): monotonic critical value, VGI critical can be defined dR monotonic Cexp(1.5 T ) d p (1) p R R VGIexp(1.5 T ) d VGIcritical ln( ) critical / C monotonic0 p monotonic monotonic where R is the average void radius; T R0 represents the stress triaxiality which is the as below: ratio of mean stress to effective stress and (5) C is a material parameter.