Load-crack Mouth Opening Displacement Curves Research Articles

Equivalence between Two Fracture Methods

Two fracture parameters, i.e., the initiation fracture energy release GIcini and the unstable fracture energy release GIcun, are termed to distinguish the different crack propagation stages. Totally ten temperatures varying from 20oC to 600oC and the specimen size of 230×200×200 mm with initial-notch depth ratios 0.4 were considered. Wedge-splitting method is adopted to measure the loadcrack mouth opening displacement curves (PCMOD) and double-G fracture parameters are experimentally determined. In order to verify the feasibility of this model in post-fire concrete, the effective double-K fracture parameters converted by double-G fracture parameters using are compared with the double-K fracture parameters.

Fracture Behaviors of Post-Fire Concrete

nvestigations on the residual Mode-I fracture behaviors of concrete subjected to elevated temperatures were implemented in present research. Test specimens of the same dimensions, 230×200×200 mm, were exposed to ten temperatures varying from 20oC to 600oC. The wedge splitting method was employed to obtain the complete load-crack mouth opening displacement curves (P-CMOD) of the post-fire specimens, from which the initial fracture toughness Kini, the critical fracture toughness Kic and the fracture energy GF were calculated. The results demonstrated that Kini, Kic decreased monotonically with increasing heating temperatures Tm owing to the thermal damage induced by high temperatures; whereas GF sustained a hold-increase-decrease tendency with Tm for the energy dissipation of multi-cracks.

Cohesive zone modeling of ductile tearing process in brazed joints

Ductile tearing process in low carbon steel brazed joints with copper filler metal is studied using the Cohesive Zone Model. The Cohesive Zone Model is characterized by two parameters related to the cohesive strength and cohesive energy. A new method is developed to estimate the Cohesive Zone Model parameters through direct experimental measurements and numerical modeling. The cohesive energy of the brazed joints is obtained from the fracture test results performed on the single-edge notched bend specimens. Based on the obtained cohesive energy parameter, the fracture test is simulated using a cohesive zone finite element model. A unique value for the joint cohesive strength is determined by best fitting the finite element results to the experimental load-crack mouth opening displacement curves. The merit of the characterized Cohesive Zone Model is explored by finite element modeling of the tensile test performed on the single-edge notched tension specimens. The load-crack mouth opening displacement curve obtained from the finite element modeling conforms to the corresponding tensile test results. Furthermore, the effect of the crack tip stress constraint on the plastic zone shape and size is successfully captured by the model. The good agreement between the finite element simulation results and the experimental data demonstrates the applicability of the Cohesive Zone Model for fracture analysis of the brazed joints.

Incremental displacement collocation method for the evaluation of tension softening curve of mortar

The tension softening curve (TSC), showing the relationship between the cohesive tensile stress and crack opening displacement, is the constitutive law of the cohesive crack model. Due to the difficulties in measuring local deformations around the crack tip, the TSC is usually determined inversely from the global responses such as load–deflection curve or load–crack mouth opening displacement curve of pre-notched specimens. However, the use of global responses alone in the inverse analysis usually causes problems that may affect the reliability and accuracy of the TSC which is basically a local material property. To overcome these limitations, an incremental displacement collocation method (IDCM) that is able to evaluate the TSC in a step-by-step manner is proposed in this paper. Both global and local responses of a pre-notched mortar beam, which are measured using an electronic speckle pattern interferometry technique, are used in the displacement collocation process. Furthermore, the finite element model (FEM) is utilized to simulate the response of the beam. The TSCs evaluated in this study are verified through the comparisons of the global and local displacements as well as the fracture energy. A tri-linear curve was found to be the best approximation of the TSC of mortar.

Meso-scale modelling of the size effect on the fracture process zone of concrete

The size effect on the fracture process zone in notched and unnotched three point bending tests of concrete beams is analysed by a meso-scale approach. Concrete is modelled at the meso-scale as stiff aggregates embedded in a soft matrix separated by weak interfaces. The mechanical response of the three phases is modelled by a discrete lattice approach. The model parameters were chosen so that the global model response in the form of load-crack mouth opening displacement curves were in agreement with experimental results reported in the literature. The fracture process zone of concrete is determined numerically by evaluating the average of spatial distribution of dissipated energy densities of random meso-scale analyses. The influence of size and boundary conditions on the fracture process zone in concrete is investigated by comparing the results for beams of different sizes and boundary conditions.

Residual fracture properties of concrete subjected to elevated temperatures

Investigations on the residual Mode-I fracture behaviors of concrete subjected to elevated temperatures were carried out. Test specimens with the same dimensions, 230 × 200 × 200 mm, were exposed to temperatures varying from 65 to 600°C. The wedge splitting method was employed to obtain the complete load-crack mouth opening displacement curves (P–CMOD) of the post-fire specimens, from which the initial fracture toughness Kini, the critical fracture toughness Kic and the fracture energy GF were calculated. The results demonstrated that Kini decreased monotonically with increasing heating temperature Tm; Kic and GF sustained a hold-increase–decrease tendency with Tm. Furthermore, the characteristic length lch, a brittleness parameter, was calculated and it shared the same tendency as Kic–Tm and GF–Tm. Thus, any of the three parameters could serve as the index of brittleness for post-fire concrete. The fracture parameters and other material properties of concrete could be closely related to the ultimate weight loss.

Effect of Calcium Dissolution on the Fracture Properties of Concrete Exposed to Nitric Acid Environment

The effect of calcium leaching by nitric acid on fracture properties of concrete was experimentally studied. The double-K fracture parameters were investigated using three-point bending beams, and the deterioration regularity of fracture properties of concrete chronically attacked by nitric acid was gotten on basis of these results. The load-crack mouth opening displacement curves under different nitric attack periods were obtained by pasting some strain gauges onto the pre-crack tip. On basis of the double-K criterion, the unstable fracture toughness as well as the initial fracture toughness was calculated according to the critical crack mouth opening displacement, the unstable fracture load and initial cracking load which can be obtained from the test. The experimental results indicated that the ratio of the initial fracture toughness to the unstable fracture toughness varied between 0.47 and 0.61 approximately. Both of the unstable fracture toughness and the initial fracture toughness decrease with attack period especially during the early 60 days, then drop to a stable trend gradually. In addition, the initial fracture toughness is less sensitive to acid attack compared with the unstable fracture toughness.

Determination of fracture parameters for crack propagation in concrete using an energy approach

Double- G fracture model, a new analytical model describing fracture behaviour on cracked concrete, was recently proposed by Xu and Zhao based on the conception of energy release rate. This model couples the Griffith brittle fracture theory with the bridging softening property of concrete, and it is an extension of double- K fracture model proposed by Xu and Reinhardt. In this model, two fracture parameters, i.e., the initiation fracture energy release G Ic ini and the unstable fracture energy release G Ic un , are termed to distinguish the different crack propagation stages undergoing during the whole fracture process in concrete. The difference between the two parameters, written as G Ic c , is assumed to come from the contribution by aggregate bridging interlock, which results in the presence of fracture process zone. In our present work, firstly, the new model is elaborately introduced. Then, fracture tests are conducted, where besides three-point bending beams, a new testing method, called wedge-splitting on compact tension is adopted. In the experiments, electrical strain gauges are used to measure initial cracking load. Based on recorded load–crack mouth opening displacement curve ( P– CMOD) or load–displacement curve ( P– δ) and load–strain curve ( P– ε), double- G fracture parameters are experimentally determined. Further more, based on the assumed three parameters relationship among G Ic ini , G Ic un and G Ic c , unstable fracture energy release are calculated. A comparable result between the measured G Ic un-e and the calculated G Ic un-c confirms this assumption. In order to verify the feasibility of this new model, the effective double- K fracture parameters converted by double- G fracture parameters using K = EG are compared with the double- K fracture parameters calculated by double- K fracture model. It is found that there is a good agreement. Another two series of different initial crack-depth ratios three-point bending beams carried out by Refai and Swartz are also collected to provide more experimental verification. It shows that the results obtained from the double- G fracture model agree well with those of double- K fracture model.

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76 mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125 mm/min (0.005 in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G 1). There is a well pronounced general trend observed: G 1 increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G 1 increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G 1, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.