Load-point Displacement Research Articles

Determination of parameters of a viscous-cohesive fracture model by inverse analysis

ABSTRACTThe quasi-brittle, loading rate dependent behaviour of the concrete, characterized by a fracture process zone (FPZ) ahead of the crack front, can be described through a viscous-cohesive model. In this paper, a viscous cohesive model proposed in a former paper is evaluated for a group of high strength concrete beams loaded at rates from 10-5 mm/s to 10+1 mm/s. A software has been developed to enable the automatic determination of the viscous-cohesive model parameters through inverse analysis on load-versus loading-point displacement (P-d) from threepoint bend tests on notched prismatic specimens. The strategy allowed the sensitivity analysis of the parameters related to viscous behaviour. The analysis of results shows that the formerly proposed model can be improved for a better simulation of the loading rate dependence on the cohesive fracture process.

Modeling of Experimental Atherosclerotic Plaque Delamination.

A cohesive zone model (CZM) approach is applied to simulate atherosclerotic plaque delamination experiments in mouse abdominal aorta specimens. A three-dimensional finite element model is developed for the experiments. The aortic wall is treated as a fiber-reinforced, highly deformable, incompressible material, and the Holzapfel-Gasser-Ogden (HGO) model is adopted for the aortic bulk material behavior. Cohesive elements are placed along the plaque-media interface along which delamination occurs. The 3D specimen geometry is created based on images from the experiments and certain simplifying approximations. A set of HGO and CZM parameter values is determined based on values suggested in the literature and through matching simulation predictions of the load vs. load-point displacement curve with experimental measurements for one loading-delamination-unloading cycle. Using this set of parameter values, simulation predictions for four other loading-delamination-unloading cycles are obtained, which show good agreement with experimental measurements. The findings of the current study demonstrate the applicability of the CZM approach in arterial tissue failure simulations.

Importance of Material’s Dynamic Stress Intensity Factor Calculation in the Design of High Strenght Structures

The researchers and scientists have concluded that material dynamic fracture properties must be considered during the design stage of the modern structure. The dynamic stress intensity factor is very important in understanding of material dynamic behavior. Keeping in view the importance of the materials dynamic stress intensity factor: an efficient and reliable numerical-analytical procedure is developed for calculation of dynamic stress intensity factor. For this, three-dimensional model of a Modified Hopkinson Pressure Bar (MHPB) and a specimen is modeled and analyzed with the ANSYS software. Transient dynamic analysis technique is used for simulation of load-variations as a function of time. As an output of analysis, values of load point displacement and Crack Mouth Opening Displacement (CMOD) are obtained. These values are substituted into two different analytical formulas for calculation of a dynamic stress intensity factor. The results obtained are compared with previous published results, and a good agreement is found.

Investigation of the response to low velocity impact and quasi-static indentation loading of particle-toughened carbon-fibre composite materials

This work investigates damage caused by low velocity impact and quasi-static indentation loading in four different particle-toughened composite systems, and one untoughened system. For impact tests, a range of energies were used between 25 and 50J. For QSI, coupons were interrupted at increasing loading point displacement levels from 2 to 5mm to allow for monitoring of damage initiation and propagation. In both loading cases, non-destructive inspection techniques were used, consisting of ultrasonic C-scan and X-ray micro-focus computed tomography. These techniques are complemented with instrumentation to capture force–displacement data, whereby load-drops are associated with observed damage modes. Key results from this work highlight particular issues regarding strain-rate sensitivity of delamination development and an earlier onset of fibre fracture associated with particle-toughened systems. These issues, in addition to observations on the role of micro-scale events on damage morphology, are discussed with a focus on material development and material testing practices.

On problems with the determination of the fracture resistance for materials with spatial variations of the Young’s modulus

The paper considers the near-tip J-integral \(\text {J}_{\mathrm{tip}}\), the far-field J-integral \(\text {J}_{\mathrm{far}} \), and the experimental J-integral \(\text {J}^{\mathrm{exp}}\) in a material with sinusoidal variation of the Young’s modulus \(E\). The evaluations of \(\text {J}_{\mathrm{tip}} \) and \(\text {J}_{\mathrm{far}} \) are based on the concept of configurational forces; \(\text {J}^{\mathrm{exp}}\) is evaluated from the area below the load point displacement curve, as prescribed by the standard testing procedures. Analytic expressions and/or approximation formulae are derived, how \(\text {J}_{\mathrm{tip}} ,\,\text {J}_{\mathrm{far}} \) and \(\text {J}^{\mathrm{exp}}\) depend on the system parameters of the material, i.e. wavelength and amplitude of the \(E\)-variation and its phase shift with respect to the crack tip position, and the global specimen dimensions. The analyses show that \(\text {J}_{\mathrm{tip}} \) and \(\text {J}_{\mathrm{far}} \) exhibit a strong dependency on the phase shift, but not the experimental J-integral \(\text {J}^{\mathrm{exp}}\). This is the reason why the current procedures for fracture mechanics testing are not suitable to determine the true values of the fracture initiation toughness \(\text {J}_\mathrm{i} \) or the crack growth resistance \(R\) of a material, if the material properties exhibit a spatial variation in the direction of crack propagation. Relations are given to estimate the possible errors.

New improvement of the combined optical fiber transducer for landslide monitoring

Abstract. Landslide monitoring is important in predicting the behavior of landslides, thereby ensuring environmental, life, and property safety. On the basis of our previous studies, we conducted the double shear test by using a third-generation optical fiber transducer that uses expandable polystyrene (EPS) as base material. However, the third-generation transducer has poor performance when cohesive force is present between the grout and capillary stainless steel pipe of the transducer. Thus, the fourth-generation optical fiber transducer was invented. Similar to the third-generation transducer, the fourth-generation transducer also used EPS as its base material. Single shear test was conducted on the fourth-generation transducer after being grouted with cement mortar (1 : 1 mix ratio). The micro-bend loss mechanism of the optical fiber was considered, and the optical time domain reflectometry instrument was used. The fact that the loss sequence of optical fibers subjected to loading is different at various locations is found. The relationship of the loading-point displacement vs. optical fiber sliding distance and optical loss were measured. Results show that the maximum initial measurement precision of the newly proposed device is 1 mm, the corresponding sliding distance is 21 mm, and the dynamic range is 0–20 mm. The fourth-generation transducer can measure the movement direction of loadings, thus making this transducer applicable for landslide monitoring.

Fracture behaviour of steel fibre-reinforced concrete at a wide range of loading rates

Three-point bending tests on notched beams of steel fibre-reinforced concrete (SFRC) have been conducted using both a servo-hydraulic machine and a drop-weight impact device. The shape and geometry of the beams followed the RILEM recommendation, i.e., 150 mm × 150 mm in cross section, 700 mm in length, notch-depth ratio was around 1/6 and the span of the tests was kept constant 500 mm. The peak load and the fracture energy were measured over a wide range of loading rates (loading point displacement rates), spanning six orders of magnitude. Under low loading rates, from 10−3 mm/s to 100 mm/s, the tests were performed with the servo-hydraulic machine; from 102 mm/s to 103 mm/s, the drop-weight impact machine was used instead. The results show that the fracture energy and the peak load increase as the loading rate increases. Furthermore, such a trend is relatively mild under low rates. The gain of the fracture energy and peak load is around 10% compared with its quasi-static values. It could be attributed to viscous effects mainly originated by the presence of free water in voids and porous structures in the matrix, and the weak fibre pullout resistance. However, under high rates the increases in the fracture energy and the peak load are pronounced due to the inertia effect and the greater fibre pullout energy. The dynamic increase factors of the peak load and the fracture energy for the fastest loading rate are approximately 3.5 and 2.5, respectively.

An Experimental-Numerical Hybrid Method to Determine Dynamic Elastic-Plastic Fracture Toughness

The dynamic fracture behavior of 7075-T6 aluminum alloy was studied by finite element method to simulate a cracked three-point bending specimen loaded by stress wave loading. In order to determine the elastic-plastic dynamic fracture toughness using quasi-static fracture mechanics theory, the nominal load measured by Hopkinson pressure bar loaded fracture testing system was input into a finite element program to calculate the loading point displacement, and then this displacement was employed to obtain the load-displacement field in the vicinity of the crack tip without the inertia effect, the variation of J-integral as a function of time was established using the load-displacement parameters determined by finite element analysis. The critical J-integral corresponding to crack initiation time detected by a small strain gauge mounted on the three-point bending fracture specimen is determined as an elastic-plastic dynamic fracture toughness (JId). The comparison between the equivalent dynamic fracture toughness(KId) given by the aforementioned procedures and the value measured in previous studies was made to verify the validation of the proposed procedure.

Effect of fluid salinity on subcritical crack propagation in calcite

The slow propagation of cracks, also called subcritical crack growth, is a mechanism of fracturing responsible for a ductile deformation of rocks under crustal conditions. In the present study, the double-torsion technique was used to measure the effect of fluid chemistry on the slow propagation of cracks in calcite single crystals at room temperature. Time-lapse images and measurements of force and load-point displacement allowed accurate characterization of crack velocities in a range of 10−8 to 10−4m/s. Velocity curves as a function of energy-release rates were obtained for different fluid compositions, varying NH4Cl and NaCl concentrations. Our results show the presence of a threshold in fluid composition, separating two regimes: weakening conditions where the crack propagation is favored, and strengthening conditions where crack propagation slows down. We suggest that electrostatic surface forces that modify the repulsion forces between the two surfaces of the crack may be responsible for this behavior.

Creep constitutive model considerations for high-temperature finite element numerical simulations

Finite element modelling is increasingly used as an integral part of creep analyses for the integrity assessment of high-temperature structures. An important consideration in such finite element simulations is the constitutive model used to represent the creep strain response of the component material as a function of temperature, stress and time. There are a variety of creep models which can be chosen by the analyst for implementation in finite element codes. In this study, five different creep models have been fitted to a set of experimental uniaxial creep curves for a 1%CrMoV turbine rotor steel at 550 °C. Subsequently, the derived constitutive equations have been implemented in finite element model representations of a series of fracture mechanics compact tension specimens manufactured from the same heat of the steel and loaded at the same temperature. The outcome clearly demonstrates the potential sensitivity of high-temperature numerical analyses of structures to the type of creep model adopted, and to the scope of the experimental data from which the model is derived. This is shown by comparing the load point displacement records from a number of compact tension specimen creep crack incubation tests with the results of finite element simulations employing the different creep deformation models. FE calculated steady-state creep stress/strain distributions ahead of the notches of compact tension specimens can also exhibit a strong sensitivity to the type of creep model adopted. Prior benchmarking the effectiveness of finite element simulation procedures for critical high-temperature components with the selected material creep model equation is therefore strongly recommended.

Stability of beam-like fracture mechanics specimens

Test specimens used to determine the interlaminar strength of composites as well as the strength of adhesive layers are known to occasionally suffer from instability. Thus, even though the experiments are performed under controlled load-point displacement, the experiments are terminated prematurely by unstable crack propagation. Often there exists a critical crack length which must be exceeded in order to obtain stable crack propagation. In this paper, a general method to assess the stability of beam-like fracture mechanics specimens is developed. Both systems subjected to a single load and the more general situation with several independent loads are treated. A simple formula is derived for the critical crack length for one-parameter loading. The only parameter necessary as input is the compliance of the un-cracked specimen. For the case of non-proportional loading, stability is determined by studying the eigenvalues of a symmetric matrix. Other findings quantified in the paper are the effect of orthotropy, the influence of a flexible interphase layer and the influence of the compliance of the loading device.

Numerical Simulation of Series Experiments of Concrete Fracture

With progress of the computer technology and numerical simulation method, the numerical simulation of the fracture process of concrete materials has become possible. In this paper, the numerical simulation models of the two types of samples were carried out with the SOLID65 concrete element based on the ANSYS software platform. According to the results, the non-linear characteristic of the concrete material exhibited in the loading process is reflected by the phenomenon that the slope of the later stage shows some reduction in the simulated load - loading point displacement curve. That is to say, the behavior of the appearance and development of cracks can be simulated with SOLID65 concrete element in ANSYS.

Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads

The behavior of concrete/reinforced concrete structures is strongly influenced by the loading rate. Reinforced concrete structural members subjected to impact loads behave quite differently as compared to the same subjected to quasi-static loading. This difference is attributed to the strain-rate influence on strength, stiffness, and ductility as well as to the activation of inertia forces. These influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend significantly on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of reinforced concrete beams with different amount of shear reinforcement under impact. The experiments reported in literature are numerically simulated using the rate sensitive microplane model as constitutive law for concrete, while the strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. However, the impact was modeled not by explicit modeling of two bodies but by incrementing the load point displacement till the maximum value and at the rate reported from the test. The results of the numerical study show that the numerical analysis using the procedure followed in this work can very well simulate the impact behavior of reinforced concrete beams. The static and dynamic reactions, crack patterns and failure modes as predicted in analysis are in close agreement with their experimentally observed counterparts. It was concluded that under impact loads, of the order as simulated in this work (blunt impact with velocity of around 1 m/s), the shear reinforcement does not get activated and therefore the dynamic reactions, unlike static reactions, are almost independent of the amount of shear reinforcement in the beams. However, the presence of shear reinforcement significantly affects the crack pattern and the cracks are well distributed in the presence of shear reinforcement, thus avoiding the formation of shear plugs.

Numerical Simulation of Fracture Process of Three-Point Bending Beam of Concrete Based on Modified Mazars Model

Taking into account the initial damage and the accumulation of damage of concrete, Mazars damage model was modified. Based on the modified Mazars damage model, combined with finite element software ANSYS, the fracture failure process of the three-point bending notched beam of concrete was simulated. The initiation load Pini and maximum load Pmax of the three-point bending beam were determined with the damage criterion, and the full relation curve of the load P versus the loading point displacement Δ of the fracture failure process of the three-point bending beam was obtained. The results show that the method of numerical simulation of concrete fracture failure process is feasible, and based on the initiation load of the crack determined by numerical simulation, the initiation toughness of the beam can be easily calculated, and the problem of calculation of the initiation toughness caused by the initiation load can not be accurately determined in the actual experiment is resolved.

The Series <i>K</i> Criterion of Unstable Fracture of Concrete and its Application

The knowledge from extensive investigations showed that the non-linearity of the load and loading point displacement curve is mainly associated with crack propagation. Based on the linear asymptotic superposition assumption, the critical effective crack length is evaluated by analyzing the nonlinear characteristics of the load and loading point displacement curves of a series of the fracture tests. Furthermore, the unstable fracture toughness is determined by inserting the peak load and the critical effective crack length into a formula developed from LEFM. Based on the calculated results, the series K criterion of unstable fracture of concrete fracture is established. At last, an engineering example of cracking analysis of the upstream lock-head foundation of the ship-lift of the Three Gorges Project is given.

Crack mouth opening displacement controlled fracture tests of brittle ceramics

Controlled fracture tests are required for the accurate determination of the toughness parameters of materials in order to assure the full conversion of the supplied energy into crack surface energy. From the three parameters involved in the test, load, displacement of the load point and crack mouth opening displacement (CMOD), this latter is the only one that continuously increases as fracture proceeds. Therefore, the CMOD has been proposed as control variable for the stable fracture tests. In this work, a new equipment to perform stable fracture tests of single edge V-notch beams (SEVNB) of ceramics in three points bending controlled by the CMOD is presented. The developed equipment allows performing stable fracture tests of extremely brittle materials. The equipment is presented together with results obtained for fine grained aluminium–magnesium aluminate and alumina ceramics.

Fracture Properties of Concrete–Concrete Interfaces Using Digital Image Correlation

The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete-concrete jointed interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement, crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis matches well with those measured experimentally.

Back‐Face Strain for Monitoring Stable Crack Extension in Precracked Flexure Specimens

Calibrations relating back‐face strain (BFS) to crack length in precracked flexure specimens were developed for different strain gage sizes. The functions were verified via experimental compliance measurements of notched and precracked ceramic beams. Good agreement between the functions and experiments occurred, and fracture toughness was calculated using several operational methods: maximum test load and optically measured precrack length; load at 2% crack extension and optical precrack length; and maximum load and BFS crack length. All the methods gave comparable results. The initiation toughness, KIi, was also estimated from the initial compliance and load. The results demonstrate that the stability of precracked ceramic specimens tested in four‐point flexure is a common occurrence, and that methods such as remotely monitored load‐point displacement are only adequate for detecting stable extension of relatively deep cracks.

Crack-front propagation during three-point-bending tests of polymethyl-methacrylate beams

Crack-front evolution in polymethyl-methacrylate (PMMA) beams was measured during quasi-static three-point-bending tests performed on a universal testing machine. A high-speed camera was used to record the crack-front propagation process through the specimen thickness and to determine the instantaneous crack-length during the test, considering the effect of different initial notch lengths and loading-point displacement rates. The average steady crack-propagation speed was also calculated and correlated with the stored elastic energy, and these results have been compared with those reported by other authors for different test conditions. This experimental technique appears to be suitable to determine the influence of the test conditions on the crack-propagation speed of PMMA specimens.

Fracture behaviour of high-strength concrete at a wide range of loading rates

Three-point bending tests on notched beams of a high-strength concrete have been conducted using both a servo-hydraulic machine and a self-designed drop-weight impact device. The fracture energy and the peak load were measured over a wide range of loading point displacement rates, spanning eight orders of magnitude. Under low displacement rates, from 10 −4 to 10 mm/s, the tests were performed with the servo-hydraulic machine; from 10 2 to 10 3 mm/s we used the drop-weight impact machine. The results show that the fracture energy and the peak load increase as the loading rate increases. Nevertheless, such a trend is relatively slight under low rates and can be attributed to viscous effects mainly originating from the presence of water in the pore structure. Under high rates the increases in the fracture energy and in the peak load are dramatic due to the effect of inertia.