Dynamic SIF Research Articles

A two-level nesting smoothed extended meshfree method for dynamic fracture analysis

A two-level nesting smoothed extended meshfree method (S-XMM-N) is presented for modeling dynamic fracture behaviors in two-dimensional linear elastic solids. The extended meshfree method based on the partition of unity allows for arbitrary discontinuities, but with low computational efficiency needs improvement. Meanwhile, directly introducing the generalized smoothed strain technique into the extended meshfree method can save more computational times, and with low accuracy also improvement. The proposed method combined the best feature of both the recently developed two-level nesting smoothing meshfree method and the extended radial point interpolation method (XRPIM). On the one hand, the S-XMM-N saves much more computational time than XRPIM by using the proposed two-level nesting triangular sub-domains smoothing integration, where only fewer integration points are employed and the derivatives of shape functions do not need to be calculated for constructing the stiffness matrix. On the other hand, the computational accuracy can be ensured due to the employment of Richardson extrapolation method. The results for the static and dynamic SIFs are compared with the analytical and other numerical solutions by several benchmark fracture problems.

Solar-induced chlorophyll fluorescence intensity has a significant correlation with negative air ion release in forest canopy

Forest vegetation is an essential source of negative air ion (NAI) and influencing factor of the process. A number of studies have focused on the temporal and spatial changes of NAI in different forest communities and their relationship with meteorological factors; however, there is no literature on the relationship between solar-induced chlorophyll fluorescence intensity (SIF) and NAI, and quantitative research on relationship between NAI and photosynthesis of forest vegetation is comparatively limited. In this study, we investigated the dynamic changes NAI, SIF, and meteorological parameters in canopy during the growing season by using a flux tower at the sites Xiaolangdi and Minquan in a warm-temperate monsoon climate zone from June to September of 2019 and 2020. Results showed that the canopy NAI, SIF, and photosynthetically active radiation (PAR) showed significant diurnal and seasonal dynamic change characteristics, and that the changes in the observed indicators at different times were significantly different. The seasonal change characteristics of canopy NAI and SIF were relatively similar, and canopy SIF could accurately capture the dynamic changes of NAI. Additionally, the NAI–SIF relationship was increasingly significant at higher PAR levels, and the coefficient of determination (R2) of the two sites reached 0.652 and 0.570. It showed that when vegetation photosynthesis was fully activated, the dynamic change process of the canopy NAI provided a more robust correlation and more accurate estimation in the vegetation's main growth stage, thus demonstrating the reliability of SIF as an indicator for tracking NAI seasonal changes. In the future, automatic, continuous SIF observations could provide reliable understanding of the photosynthetic characteristics of terrestrial ecosystems, thereby quantifying the contribution potential of forest to NAI application in ground-based optical measurement and airborne and satellite remote sensing. This provides a working foundation for direct assessment of spatial and temporal distribution patterns of global seasonal NAI.

Effect of loading rates on crack propagating speed, fracture toughness and energy release rate using single-cleavage trapezoidal open specimen under impact loads

The former studies indicate that loading rates significantly affect dynamic behavior of brittle materials, for instance, the dynamic compressive and tensile strength increase with loading rates. However, there still are many unknown or partially unknown aspects. For example, whether loading rates have effect on crack dynamic propagating behavior (propagation toughness, velocity and arrest, etc). To further explore the effect of loading rates on crack dynamic responses, a large-size single-cleavage trapezoidal open (SCTO) specimen was proposed, and impacting tests using the SCTO specimen under drop plate impact were conducted. Crack propagation gauges (CPGs) were employed in measuring impact loads, crack propagation time and velocities. In order to verify the testing result, the corresponding numerical model was established using explicit dynamic software AUTODYN, and the simulation result is basically consistent with the experimental results. The ABAQUS software was used to calculate the dynamic SIFs. The universal function was calculated by fractal method. The experimental-numerical method was employed in determining initiation toughness and propagation toughness. The results indicate that crack propagating velocities, dynamic fracture toughness and energy release rates increase with loading rates; crack delayed initiation time decreases with loading rates.

A simplified method for evaluation of brittle crack arrest toughness of steels in scaled-down bending tests

The wide-plate crack arrest test under tensile load for characterizing the brittle crack arrest toughness of high strength shipbuilding steel requires high economical cost and long lead-time, so there is still a substantial industry need for the simplified evaluation using the scaled-down specimen. The alternative method using a single edge-notched bending specimen, which assumes the complete load redistribution during the crack propagation, was recently proposed. However, it was confirmed that the results obtained using this method exhibited a low correlation with the arrest toughness obtained using the wide-plate tests. A new scaled-down version of the crack arrest test under bending load and a series of simplified evaluation based on the dynamic elasto-plastic FEA were introduced to characterize the crack arrest performance of the two types of steel plates in this investigation. The specimen is a single edge-notched tapered plate subjected to a three-point bending load in an isothermal environment. The geometry was selected so that the dynamic crack driving force calculated using FEA decreases monotonically with the crack propagation. For adopting a simplistic analytical approach considering the dynamic effect, the dynamic FEA simulation assumed the constant crack velocity and flat crack front and output the opening stress distributed ahead of the growing crack. The experimentally obtained values of the arrested crack length and the analytically obtained transition curves of the dynamic SIF were employed to characterize the crack arrest performance of the two steels. The results obtained using the simplified method developed in this investigation exhibited a high correlation with the arrest toughness obtained using the wide-plate crack arrest test.

Improved XFEM: Accurate and robust dynamic crack growth simulation

The extended finite element method (XFEM) is widely accepted in academy as the major technique for crack analysis. Starting from 2009, commercial codes started to use this technique for crack analysis, singling the mature and acceptance of the technique in industries. However, the direct extension of the singular tip enrichment of XFEM, the core of the method, to dynamic crack growth simulation has long been a difficulty due to: (a) elevated bad conditioning as crack propagating, (b) extra-dof dynamics and energy inconsistency, and (c) “null” critical time step size and optimal mass lumping at crack tip. Based on an extra-dof-free partition of unity enrichment technique (Tian, 2013), we have improved XFEM through a crack tip enrichment without extra dof (Tian and Wen, 2015). This paper is to answer the question whether the improved XFEM can also be easily extended to dynamic problems. Numerical tests show that the new XFEM is not only straightforward in implementation in dynamic problems, also provides the most accurate dynamic SIF in the benchmark problems and is orders of magnitude faster with an iterative solver.

Modeling of Brittle Crack Propagation/Arrest Behavior in Steel Plates

To prevent brittle cracks from causing fatal damage to steel structures, it is needed that steels have enough crack arrestability. However, the brittle crack propagation/arrest behavior has not been explained theoretically enough from the aspect of energy balance and especially the long crack problem has remained as an important unsolved issue for some decades. The authors propose a new model based on local fracture stress criterion to solve the long crack problem. The model considers crack closure effect by uncracked side ligaments formed due to relaxation of plastic constraint progressing with SIF increasing. A simultaneous equation composed of four equations, which formulate local fracture condition, strain hardening, yield point, and dynamic SIF considering side ligaments, is solved to simulate a crack propagation in the model. To validate the model, we compared model simulations with some experiments. Some of them were conducted under the long crack problem condition and obtained the result that they showed good agreements, even under the long crack problem condition. This implies the long crack problem can be explained from the aspect of side ligament development due to the relaxation of plastic constraint.

Determination of History of Dynamic Stress Intensity Factor at Low Impact Velocities using Reduced Record of Experimental Forces in Three Point Bend Test

The paper examines the possibility of reducing the efforts for data collection through impact testing of three point bend specimens for determining the variation of the dynamic SIF (DSIF) with time. In modelling, the specimen is represented by two Timoshenko beams connected by a rotational spring. The DSIF variation with time is obtained through forced vibration analysis by treating the beam as a free-free system under the action of the experimentally measured striker force and the anvil reactions. The anvil reactions can correspond to any specimen in a batch of specimens differing slightly in length or crack size.

Dynamic fracture analysis technique of aircraft fuselage containing damage subjected to blast

This paper primarily presents the development and application of automation computational analysis techniques to determine the dynamic stress intensity factor for the damaged aircraft fuselage subjected to two kinds of blast load. A program based on an automated procedure to simulate a cracked fuselage is developed. It may create a 3-dimensional panel model using parametrisation. The stress around the crack tips will be captured and the dynamic stress intensity factor can be obtained at every moment of the blast automatically. A typical curved panel model which consists of 7 frames and 8 stringers is calculated. The calculation results show that the form of the dynamic SIF curve is similar to that of the load curve while the peak point of the dynamic SIF curve occurs a little later than that of the load curves due to the inertia effect. The longer the crack is, the more obvious the effect is. The peak SIF value of the crack under blast load is bigger than that under the static load for certain crack length. The longer the crack is, the bigger the difference between the dynamic peak SIF value and static SIF is. At the same time, the load time has an effect on the dynamic SIF curve and its peak value. These results show good agreement with theoretical principles.

Forced Vibration Analysis in the Context of Dynamic SIFs in Impact Bending Tests

Motion of a Timoshenko beam with a crack is analyzed by representing it through a massless rotational spring. This is relevant for evaluation of dynamic stress intensity factor (DSIF) in one- or three-point impact bend tests. The model predictions compare well with experimental results reported in the literature.

Influence of loading rate on dynamic fracture behavior of fiber-reinforced composites

The effect of loading rate on the dynamic fracture properties and the failure mechanisms of glass fiber-reinforced composite materials under mode I fracture is studied. Dynamic reflective caustic experiments are carried out for two loading rates. By measuring the characteristic dimensions of the shadow spots during the caustic experiments, the dynamic SIFs are calculated for different loading rates. The experimental results indicate that the dynamic fracture toughness K Id increases remarkably with increasing loading rate, and the crack grows faster under the high-velocity impact. Moreover, by examining the crack growth routes and the fracture surfaces, it is shown that the loading rate also greatly affects the failure mechanisms at micro-scale.

Fracture Analysis for Damaged Aircraft Fuselage Subjected to Blast

This paper primarily presents the development and application of automation computational analysis techniques to determine the dynamic stress intensity factor for the damaged aircraft fuselage subjected to triangle blast load. A program based on automated procedure to simulate cracked fuselage is developed. It may create 3-dimention panel model using parameterization. The stress around the crack tips will be captured and the dynamic stress intensity factor can be obtained at every moment of the blast automatically. A typical curved panel model which consists of 7 frames and 8 stringers is calculated. The calculation results shown that the form of the dynamic SIF curve is similar to that of the triangle load curve while the peak point of dynamic SIF curve occurs a little later than that of the load curve due to the inertia effect. The longer the crack is, the more obvious the effect is. The peak SIF value of the crack under blast load is bigger than that under the static load for certain crack length. The longer the crack is, the bigger the difference between the dynamic peak SIF value and static SIF is. At the same time, the load time has effect on the dynamic SIF curve and its peak value. These results show good agreements with theoretical principles.

Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating

The concepts and classification are brought forth for the strong-discontinuous interface, the weak-discontinuous interface, the micro-discontinuous interface and the all-continuous interface. The mechanical model is established for the dynamic fracture problem of the weak-discontinuous interface between a FGM coating and a FGM substrate. The Cauchy singular integral equation for the crack is derived by integral transform, and the allocation method is used to get the numerical solution. Analysis of the numerical solution indicates that the weak discontinuity is an important factor affecting the SIFs of the interfacial crack. To reduce the weak discontinuity is beneficial to the decrease of the SIFs. Contrast between the solution of the weak-discontinuous interface and that of the micro-discontinuous one shows that the micro-discontinuity is a kind of connection relation of mechanical property better than the weak discontinuity for the coating–substrate structure. To make the interface be micro-discontinuous is helpful to enhance the capacity of the functionally gradient coating–substrate interface to resist dynamic fracture. The first rank micro-discontinuity is enough to reduce the SIFs notably, however, the higher-rank micro-discontinuous terms, which is equal to or higher than the second rank, have less effect on the SIFs. In addition, the thickness of the coating and the substrate and the applied peel stress are also important factors affecting the dynamic SIFs.

Fracture behaviour of cracks in piezoelectric media with electromechanically coupled boundary conditions

Existing studies on slit crack problems have been limited mostly to the electrically impermeable and permeable crack models, which represent the limiting cases of the physical boundary condition. This paper studies the generalized plane problem of a crack in a piezoelectric medium, with the electric boundary condition along the crack surfaces being governed by its opening displacement. The theoretical formulation of this nonlinear problem is based on the use of Fourier transforms and the solution of a system of integral equations, which are solved using Chebyshev polynomials. The analytical solution of the problem clearly shows the transition between permeable and impermeable models with increasing crack opening. Depending on the applied mechanical and electric loads, different modes of crack deformation are predicted and discussed.

MODAL APPROACH FOR PROCESSING ONE‐ AND THREE‐POINT BEND TEST DATA FOR DSIF–TIME DIAGRAM DETERMINATION. PART II—CALCULATIONS AND RESULTS

In Part I of this paper, using the modal superposition method, equations for dynamic SIF calculations are derived for an arbitrary linear model of an impact bend specimen. In this paper (Part II), modal parameters and other data which are necessary for the DSIF determination have been calculated for three types of specimen model: the Euler–Bernoulli beam model, and two‐ (2D) and three‐dimensional (3D) solid models. For the latter two cases, calculations were performed using the finite element program ADINA. Results for the 2D model of the specimen were fitted by polynomials for a wide range of specimen geometry parameters and Poisson’s ratio values. Considerable differences were observed between the beam model parameters and the 2D or 3D ones. The differences in results for the 2D and 3D models are small and mainly connected with non‐uniformity of the SIF distribution along the front of a through‐crack in the 3D solid. Results of processing one‐ and three‐point bend test data reported in the literature are presented. Numerical DSIF values are compared with the experimental ones.

Time-harmonic body force loading of a mode-II penny-shaped crack in an elastic solid

The axisymmetric problem of determining the dynamic stress intensity factor for a penny-shaped crack in an infinite elastic medium subjected to the action of time-harmonic radial shear body forces is considered in the present paper. The solution of the problem is obtained by superposition of the solutions of two simpler problems. the first of these problems corresponds to the unperturbed or crackless infinite space under the prescribed body forces, while the second problem consists in determining the stress intensity factor for the penny-shaped crack whose faces are directly acted upon by some shear stresses. The form of these stresses is determined from the solution of the first problem. Fourier and Hankel transforms have been employed to solve the first problem. Next by means of Hankel transform, the second problem has been reduced to a pair of dual integral equations, which have been subsequently transformed into a Fredholm integral equation of the second kind via an auxiliary function. The integral equation has been solved numerically to determine the variations of the dynamic SIF at the vicinity of the penny-shaped crack for the case where the elastic space is subjected to symmetrically placed time-harmonic radial shear body forces linearly varying with the radius of the crack.

Numerical simulation of anvil interactions in the impact testing of notched bend specimens

The dynamics of impact Charpy specimen is analyzed using a finite element model. By introduction of a spring to represent the contact deformations at the support and by inclusion of a gap element, the model accounts for the effects of support reactions, specimen loss-of-contact with the anvil and influence of beam overhangs. Two approaches are investigated with the basic model; measured tup force is applied as input to predict the dynamic SIF in the first approach and the tup load itself is predicted using load-point displacement in the second. The model is validated by comparison with the experimental results published by Bohme and Kalthoff [1].

On the effects of higher vibration modes in the analysis of three point bend testing

Influence of higher modes of vibration in the dynamic analysis of impact three point bend specimen based on Euler-Bernoulli and Timoshenko beam theories are investigated in an attempt to predict the oscillatory behavior seen in the measured dynamic SIF history. Forced vibration of the cracked beam is analyzed by normal mode summation method. Contact force history computed using fundamental mode approximation is applied as input forcing function and the computed SIF histories are compared with finite element model and experimental data. Analytical and finite element results show that modes higher than the third have practically no influence on the notched beam response.

Time-harmonic body force loading of a mode-I penny-shaped crack

The present paper is concerned with the problem of determining dynamic SIF of a penny-shaped crack in an infinite elastic medium, which is subjected to the action of time-harmonic axial body forces, placed symmetrically with respect to the crack plane. The solution of the problem is obtained by superposition of the solutions of two simpler problems. The first of these problems is related to the unperturbed (crackless) space under the prescribed axial body forces, while the second problem consists in finding the dynamic SIF of the penny-shaped crack whose faces are directly acted upon by some axial stresses. The form of these axial stresses is determined from the solution of the first problem. Fourier and Hankel transforms have been used to solve the first problem. Next by means of the Hankel transform, the second problem has been reduced to a pair of dual integral equations which have been subsequently transformed into a Fredholm integral equation of the second kind via an auxiliary function. The integral equation has been solved numerically in order to determine the variations of the dynamic stress intensity factor at the rim of the penny-shaped crack for some particular body force loading cases.

A penny-shaped crack under time-harmonic torsional body forces

The problem of determining dynamic SIF for a penny-shaped crack embedded in an infinite elastic medium in which time-harmonic torsional body forces are available is investigated in the present paper. The solution of the title problem is obtained by superposition of the solutions of two simpler problems. The first problem corresponds to the unperturbed (crackless) infinite elastic medium subjected to the action of the prescribed torsional body forces, while the second problem consists in finding the dynamic stress intensity factor for the penny-shaped crack whose faces are subjected to some torsional loads. The form of these torsional loads are determined from the solution of the first problem. The solution of the first problem is obtained by using Fourier and Hankel integral transforms. The second problem has been reduced to a pair of dual integral equations by means of Hankel integral transform. The dual integral equations have been subsequently transformed into a Fredholm integral equation of the second kind via an auxiliary function, which has been solved numerically to determine the dynamic SIF at the rim of the penny-shaped crack for the case of linearly varying torsional body forces placed symmetrically with respect to the crack plane.

A study of an application of BIEM to dynamic SIF analysis.

An analytical approach plays an important role in evaluation of fracture toughness of materials and strength of flawed components under the condition of dynamic loading. The present work is an attempt to apply BIEM, in which the derived constraint equations are functions of the Laplace transform parameter, to dynamic SIF analysis. Some remarks are obtained for the series expansions of the kernels and the relationship between time-space solutions and the discretization interval of the Laplace transform parameter. Utilizing the extrapolation method, a calculation is carried out for the dynamic SIF of a crack located on an inner surface of piping.