Research paperMicromechanics of fracture and failure in concrete under monotonic and fatigue loadings
Introduction
Concrete being one of the most widely used construction material, has decades of research orbiting around it in a quest to comprehend its intricate fracture and failure mechanisms. Cogent arguments put forward by the scientific community has led to a broad consensus regarding the existence of an inelastic zone in the fracture front called the fracture process zone (FPZ). This zone encapsulates toughening mechanisms such as micro-cracking, aggregate bridging, crack branching and crack deflection which characterises the quasi-brittle nature of concrete. Based on the type of loading, the fundamental features of concrete fracture show different behaviour. Concrete members subjected to monotonically increasing displacement exhibits an extensive softening after attaining its peak load. On the contrary, three phase progressive damage followed by sudden failure is observed when subjected to fatigue loading. This conflicting fracture response of concrete under different loading conditions warrants further exploration of the formation of FPZ. This paper aims to describe the similarities and differences in the fracture process zone formed in plain concrete subjected to monotonic and fatigue loadings through an experimental investigation.
Numerous experimental methods have been used to determine the size of FPZ and its influence on the fracture behaviour of concrete. Castro-Montero et al. (1990) performed experiments with laser holographic interferometry combined with digital image analysis. Their experiments have revealed that the FPZ is of constant size regardless of the length of crack and it translates along with crack extension. Maji et al. (1990) assessed the FPZ with acoustic emission technique and concluded that it has a considerable width when compared to other specimen dimensions. The acoustic emission (AE) technique has been used by several researchers (Landis, 1999, Ouyang, Landis, Shah, 1991) as it visually enables us to understand the evolution of micro mechanisms in the interior of concrete. Landis (1999) related the micro and macro fracture mechanisms in concrete through AE technique. The experiments conducted by Otsuka and Date (2000) on concrete under tension with the aid of AE technique and X-rays using a contrasting medium showed the existence of total energy zone (TEZ) which encapsulates all the micro and macro events. The FPZ and fracture core zone (FCZ) constitutes almost 95% and 70% of total energy zone, respectively. Furthermore, Otsuka also studied the influence of maximum aggregate size, specimen size and ligament size on the FPZ of concrete. The FPZ and FCZ formed in concrete is shown in Fig. 1.
Grassl et al. (2012) analysed the size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams by a meso-scale approach. They concluded that for unnotched specimen the width of FPZ increases with specimen size and for notched specimen the width of FPZ does not depend on its size. Yu et al. (2018) proposed a three-dimension realistic numerical modelling method to study the fracture mechanisms of concrete at micro or meso scale under complex loading conditions. They used X-ray computerized tomography and improved digital image processing (DIP) for the three-dimensional modelling. Alam and Loukili (2020) experimentally investigated the effect of micro-macro interaction on softening behaviour of concrete fracture using digital image correlation (DIC) and AE techniques. Based on their experimental observations they proposed an improved cohesive crack model where a damping transient stress due to micro-macro interaction is added to the cohesive stress.
All the qualitative and quantitative studies on concrete fracture has confirmed the existence of FPZ and its influence on the fracture properties of concrete under monotonic loading through various experimental investigations. However, for concrete subjected to fatigue loading the formation of FPZ has not been confirmed and it is still an ongoing research problem. Fatigue is a phenomenon wherein structures such as bridges, pavements, airport runways are subjected to repetitive loads which causes progressive and permanent internal damage in the material leading to sudden failure. Due to variability in loading and the material heterogeneity, the damage quantification of concrete under fatigue loading poses a daunting challenge for researchers. Fatigue experiments on concrete have shown three stages of damage evolution (Bazant, Xu, 1991, Carpinteri, Spagnoli, Vantadori, Viappiani, 2008). The first stage occurs due to the coalescence of internal micro cracks present in the pristine state of concrete. The second stage is a dominant phase illustrating a stable and gradually increasing state of damage due to the formation of micro cracks and this stage constitutes 90% of the total fatigue life. The third stage of damage shows an unstable state due to the coalescence of micro cracks to form a dominant macro crack. The theories of fracture and damage mechanics have been widely utilized to model the fatigue behaviour of concrete (Bazant, Xu, 1991, Keerthana, Chandra Kishen, 2018, Nguyen, 2008, Ray, Chandra Kishen, 2011). The crack size during fatigue crack propagation in concrete is computed indirectly through the compliance method (Swartz, Go, 1984, Toumi, Bascoul, 2002) which is based on the concepts of linear elastic fracture mechanics (LEFM). The fatigue failure criterion is often established based on the concept of static envelope curve (Jun, Stang, 1998, Kolluru, O’Neil, Popovics, Shah, 2000). As the experimental evidences depict a conflicting fracture behaviour in concrete under fatigue and monotonic loadings, the fracture process zone formation in concrete under fatigue has to differ from the one that forms under monotonic loading.
The main objective of this paper is to address different fracture mechanisms involved in the formation of FPZ in concrete subjected to flexural monotonic and fatigue loadings through an experimental investigation with the aid of acoustic emission (AE) and digital image correlation (DIC) techniques. Experiments are conducted on geometrically similar plain concrete notched beams of three different sizes. The specimens are tested under a simulated variable amplitude loading and constant amplitude loading. Surface displacements and crack lengths are computed using the DIC technique. The evolution of micro cracks in the interior of the specimen is obtained through AE technique. The work presented in this paper is structured as follows: The experimental program detailing the materials used for specimen preparation and the test set-up are described in Section 2. Comparison of mechanical results of monotonic and fatigue experiments are presented in Section 3. Damage evolution analysed through AE and DIC techniques are presented in Section 3. Characterisation of FPZ is presented in Section 4. The AE based b-value analysis for monotonic and fatigue load cases are discussed in Section 6. Damage index for concrete under fatigue is proposed based on the AE data and presented in Section 7. Finally, in Section 8, the summary and the main conclusions drawn from this research are presented.
Section snippets
Materials and test specimen used
The concrete specimens are prepared according to mix design procedure given in the Indian standard code of practice. Two mix designs are considered in order to compare the test results of concrete of varying strength. The first mix with cube compressive strength (fck) of 56 MPa, is used for preparation of specimens of three different sizes - small, medium and large and the second mix with cube compressive strength of 38 MPa is used for the preparation of only medium sized specimens. The mix
Comparison of monotonic and fatigue experimental results
The load-CMOD curves obtained from monotonic and fatigue tests are shown in Fig. 6 (a)-(b) and (c)-(d) respectively. The specimens of mix 1 and 2 under monotonic loading show a typical post-peak softening behaviour. This is attributed to the formation of fracture process zone where various energy dissipative mechanisms occur. The average peak load along with standard deviation and fracture energy computed according to RILEM (RILEM committee, 1985) procedure is shown in Table 2.
The load-CMOD
Evolution of damage in concrete from acoustic emission and DIC
Initiation and propagation of micro cracks dissipate energy of different magnitude depending on their size and location. This dissipated energy is captured through AE sensors which give us information on internal micro mechanisms. The micro cracks formed in the specimen gradually coalesce to form a macro crack which propagates leading to failure. The propagation of macro crack is visualised through surface displacement plots obtained through DIC analysis. In this research, AE parameters such as
Characterization of FPZ size
Several approaches based on AE technique have been proposed in the literature to characterize the size of FPZ. Lertsrisakulrat et al. (2001) and Watanabe et al. (2004) proposed different simplified empirical relations to compute localized compressive fracture length. They considered the length of FPZ to be equal to the zone with local energy greater than 15% of total energy of the specimen or the region where the distribution of peak amplitude or when AE energy is greater than 30% of the total
AE based b-value analysis
A close analogy exists between AE data produced from the fracture processes occurring in the brittle material and the seismic waves caused during the earthquakes. In seismology, seismic signals emitted due to earthquakes are related to the cumulative number of seismic events through the Gutenberg-Richter(GR) relationship which is expressed as Gutenberg and Richter (1950):where Nc is the number of seismic events, ML is the Richter magnitude of events, ′a′ and ′b′ are empirical
Damage index based on AE data
Acoustic emission provides high sensitivity real-time health monitoring and is widely employed in concrete bridges for condition assessment and damage characterization. Under fatigue loading conditions, concrete structures are prone to cracking at early stages of service life which cannot be characterized from the global response. In such situations, the ability of AE technique in early detection of cracks is useful for condition assessment of structures and prevent possible catastrophic
Summary and conclusions
In this research, fracture and failure mechanisms of concrete under monotonic and fatigue loadings are experimentally investigated. Concrete beam specimens are tested under three point bending with the aid of digital image correlation (DIC) and acoustic emission (AE) techniques. The important conclusions drawn from this research are:
- (1)
The mechanical, AE and DIC results have shown that the fundamental mechanics of fracture is different for concrete subjected to monotonic and fatigue loadings. The
CRediT authorship contribution statement
K. Keerthana: Methodology, Investigation, Data curation, Formal analysis, Writing - original draft. J.M. Chandra Kishen: Conceptualization, Methodology, Supervision, Resources, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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