Load Separation Principle Research Articles

A method to evaluate ductile fracture toughness based on load separation principle

AbstractIn combination with load separation principle, the P‐V curves of blunt‐notched specimens with different stationary cracks can be explicitly expressed as a unified formula. Further, a load separation‐based direct calibration (LSDC) method to predict instantaneous crack size and J‐resistance curve of growing cracked specimen has been developed. Two specimen configurations, compact tension and single edge‐notched bending, which are made of Cr2Ni2MoV and Q345B, respectively, are employed to verify the validity of LSDC method. The results show that the estimated J‐resistance curves are more reasonable in comparison with those obtained by unloading compliance and normalization method.

Analysis of the conditions for the occurrence of the effect of a minimum of friction in hybrid bearings based on the load separation principle

Reliability of rotating machinery is determined to a considerable degree by the bearing units. For several applications the requirements in rotational speed, bearing load and maximal vibration level are so extreme that neither rolling-element bearings nor fluid-film bearings could provide necessary operating characteristics during all regimes of operation. Hybrid bearings, which are a combination of rolling-element and fluid-film bearings, can improve performance characteristics and reliability of the rotor-bearing systems. A hybrid bearing, where a rolling-element bearing and a fluid-film bearing are positioned parallel to the vector of external load (PLEX), has the following advantages compared to a single bearing, whether rolling-element or fluid-film one: increase of life expectancy, load capacity increase, friction reduction, thermal regime enhancement, increase of stiffness, and damping properties. The present paper presents the results of theoretical and numerical research of friction characteristics of PLEX in mixed sliding and rolling friction, i.e. combination of viscous and rolling contact friction, regime. The conditions of minimum friction effect occurrence have been substantiated, and rational relations between characteristics of hybrid rolling-element bearings and fluid-film bearings needed for provision of such effect have been experimentally proven. Finally, the paper presents recommendations regarding design of such hybrid bearings for heavily loaded bearing nodes of rolling mills.

Normalization method for evaluating J-resistance curves of small-sized CIET specimen and crack front constraints

Based on dimensionless load separation principle, the normalization method for estimating J-resistance curves of CIET specimen for ductile materials has been developed. Experiments of ductile crack growth resistance on a typical pressure vessel steel SA-508 are conducted by using CT, SEB and CIET specimens. The resulted J-resistance curves show outstanding influence by load configuration and specimen dimensions. J-Q-M and J-A2-M approaches are introduced to quantify the crack front constraint of the three types of specimens. According to finite element analyses (FEA) under plane strain and 3D conditions, the distance-independent constraint parameters are calibrated by matching the FEA results with the J-Q-M and J-A2-M solutions using weight average method. The analyses show that the parameters of Q and A2 are load-independent under plane strain condition, but under 3D condition, the J-A2-M approach is incapable of characterizing the stress and deformation fields ahead of crack front of CIET specimen for SA-508 steel, and the parameter Q is no longer load-independent. Because of different crack front constraint, the CIET specimen with B=10 mm, a0=5.8 mm gets the lowest fracture resistance while the SEB specimen with B=20 mm, a0=11 mm and the CT specimen with B=15 mm, a0=29 mm obtain the highest fracture resistance for SA-508 steel. The size requirements of J-Q-M dominance for each used CIET, CT and SEB specimens are got. Finally, the constraint-modified J-resistance curves of SA-508 steel based on J-Q-M approach are constructed to predict the crack growth resistance for any fracture specimens or actual flawed structures.

Improved normalization method for ductile fracture toughness determination based on dimensionless load separation principle

This study successfully deals with the inhomogeneous dimension problem of load separation assumption, which is the theoretical basis of the normalization method. According to the dimensionless load separation principle, the normalization method has been improved by introducing a forcible blunting correction. With the improved normalization method, the J-resistance curves of five different metallic materials of CT and SEB specimens are estimated. The forcible blunting correction of initial crack size plays an important role in the J-resistance curve estimation, which is closely related to the strain hardening level of material. The higher level of strain hardening leads to a greater difference in JQ determined by different slopes of the blunting line. If the blunting line coefficient recommended by ASTM E1820-11 is used in the improved normalization method, it will lead to greater fracture resistance than that processed by the blunting line coefficient recommended by ISO 12135-2002. Therefore, the influence of the blunting line on the determination of JQ must be taken into full account in the fracture toughness assessment of metallic materials.

Non linear fracture mechanics of polymers: Load Separation and Normalization methods

Fracture toughness of ductile polymers can be measured by the incremental crack growth resistance curve, where J-Integral value is plotted as a function of crack extension. The determination of the resistance curve, J–R, is generally performed through the so-called multiple-specimen technique. In this procedure, several identical specimens are loaded to obtain different amounts of crack growth, thus involving a large number of tests and large quantity of test material. It is also hard to apply in situations such as under high-loading rate conditions, elevated temperatures and/or aggressive environments where it is difficult to stop the test to measure crack extension. Consequently, alternative single specimen techniques appear attractive. The theoretical basis for the single specimen J form used in the incremental J–R curves is given by the Load Separation Principle. It is based on the assumption that the load can be represented as the multiplication of two separate functions: a crack geometry function and a material deformation function. This principle allows the introduction of the so-called η parameter which greatly simplifies J calculation. The crack geometry function is general represented as a power law function which exponent coincides with η factor. By analyzing load line displacement records of several blunt notched specimens differing in their initial crack length before the starting of crack propagation it is possible to evaluate η factor and verify Load Separation Principle assumption. Based on the validity of this principle two methodologies have been developed: Load Separation method, S pb , and Normalization Data Reduction technique. These methodologies have the inherent advantage of developing J–R curves directly from a single load versus load-line displacement record without using any sophisticated automated crack length monitoring system. Load Separation method infers the growing crack length from the load ratio of two load–displacement records: one growing crack and other stationary crack. Normalization method utilizes the Material Key Curve, calibrated using one individual normalized load–displacement record, to infer the instantaneous crack length. Variants of both methodologies have been already successfully used in ductile fracture characterization of polymers by several authors. Innovatively here, the Load Separation Principle and the deformation function are expressed in terms of total displacement without distinguishing between elastic and plastic displacement components. Hence, calculations are simply made using the J-Integral formula based on total energy. The performance of the proposed methods is evaluated and compared with the standard multiple-specimen technique for a broad spectrum of ductile polymers. Several features of the approaches are discussed like: suitability of functional forms, influence of blunting assumption, calibration points and general limitations to their application. The results demonstrate the ease and the accurate of the Normalization method based on total displacement for ductile polymer J–R curve determination. Conversely, the great potentiality of Load Separation method relies on the special fracture cases in which the actual final crack length cannot be easily determined.

High rate toughness of ductile polymers

Impact toughness of two highly ductile polymers: acrylonitrile–butadiene–styrene (ABS) terpolymer and polypropylene block copolymer (PPBC) – was evaluated using the essential work of fracture (EWF) – and a J– R resistance single specimen curve – S pb techniques. The EWF has proved to be capable of determining toughness from the total fracture energy of several samples differing in initial ligament length and the linear regression of the data. On the other hand, the S pb method, which is based on the load separation principle, is able of constructing J– R curves by inferring instantaneous crack growth length from the sole comparison between one sharp and one blunt-notched load–displacement traces. Results show that both methodologies can be used under impact conditions when evaluating ABS polymers. However, ABS impact fracture toughness value yielded by the EWF method, w Ie, was larger than the J 0.2 value obtained from the S pb method. This difference was imputed to the more progressive development of the necking zone in front of the crack tip under plane strain conditions. On the contrary, for very ductile fracture behavior like that demonstrated by PPBC in which J-controlled conditions were not achieved and hence J– R curves could not be built the EWF appeared as a valuable alternative to characterize impact toughness.

J-R curve determination of magnesium hydroxide filled polypropylene using the normalization method

The normalization method is applied to different magnesium hydroxide filled polypropylenes. As the load separation principle is the basis of the method, its validity is checked using the load separation criterion developed by Sharobeam and Landes. Load separability is checked for all the materials when the condition of stationary crack length is fulfilled. During the determination of the deformation function using the normalization method, the large decrease of the load value of highly filled materials make it impossible to describe the load normalization variation with plastic displacement by a power law equation. Nevertheless, for the lower-filled materials, i.e. up to 40 wt% with copolymer PP and 20 wt% with homopolymer PP, the J-R curve can be determined and high concordance is found with the J-R curve obtained by multiple specimen method. The applicability of the normalization method is discussed in terms of the geometry of the plastic deformation zone. It is found that the materials that are not suitable for normalization method application are characterized by a very small plastic zone, due to the restriction of plastic flow caused by mineral filler.

Determination of J-R curve of polypropylene copolymers using the normalization method

In this paper the applicability of the load normalization method to determine J-R curves of polypropylene copolymers (PP) is analyzed. This method allows the determination of resistance curves ideally from a single fracture test, and it is based on the load separation principle, which assumes that load can be separated in two multiplicative functions, the geometry function, G(a/W), and the deformation function, H(νpl/W), which depend of the crack depth and the plastic displacement, respectively. The load separation validity has been checked for two different PP copolymers (block and random copolymers) and the load normalization method has been applied in order to determine and analyze the resistance curves, which have been compared, as a reference, with those obtained by the multiple specimen method. The applicability of the load normalization method to PP copolymers is analyzed by introducing some variations in the general procedure: Firstly, the deformation function is determined using either a power law fit or the so-called LMN function. With the power law, two different fitting methods have been tested: the usual “6 + 1” method and a “6 + 6” method proposed here for giving more weight to the final point of the curve. Secondly, the influence of the material crack tip blunting has been analyzed quantifying it through different values of the constriction factor (m) in the general expression of the blunting line. Finally, the effect of the separable blunting region extension on the J-R curve has been also analyzed by establishing different separable blunting zones.

Load separation principle in determination of J‐R curve for ductile polymers: Suitability of different material deformation functions used in the normalization method

AbstractThe load separation principle states that the load, P, can be represented as the multiplication of two independent functions: A crack geometry function, G(a), and a material deformation function, H(v). The principle constitutes the theoretical basis for the single‐specimen J‐integral experiment and the incremental calculation of J‐integral crack growth resistance (J‐R) curves. The normalization method is a new method, which assumes load separation and uses characteristic deformation properties of materials to relate load, displacement and crack length in a functional form. From the deformation material function or “material key curve”, J‐R curve can be developed from a single precracking experiment. This investigation deals with the applicability of the load separation criterion to evaluation of ductile fracture mechanics parameters in rubber‐modified polystyrene, polypropylene, rubber‐modified PMMA, ABS resin and high‐density polyethylene in the bending configuration. Different mathematical relationships for the deformation function (power law function, LMN function and combined power law straight line relationship) have been proposed and compared. The resulting J‐R curves are in good agreement with those obtained by the traditional multiple‐specimen technique. The results presented here imply that the use of a single load‐displacement method for evaluation of J‐integrals for ductile polymers is possible and hence also the normalization method can be used for evaluation of J‐R curves from a single‐test record.

APPLICATION OF A NORMALIZATION METHOD FOR DETERMINING J‐R CURVES IN GLASSY POLYMER PVC AT DIFFERENT CROSSHEAD SPEEDS

Abstract— A new single‐specimen testing method, the normalization method with the so‐called LMN calibration function, based on the load separation principle and function calibrations from an individual test record, was used to construct J‐R curves directly from load versus load‐line displacement records without any additional on‐line crack‐length monitoring equipment. The research was done on CT‐specimens of a glassy polymer PVC at different crosshead speeds ranging from 0.01 to 50 mm/min. The J‐R curves evaluated from the normalization method are in good agreement with those from the conventional multiple‐specimen testing method in the whole range of the tested crosshead speeds. The results demonstrated the applicability of the normalization method for developing J‐R curves at different crosshead speeds in PVC. The crack initiation J‐integral values, J0.2, showed a two‐regime dependence on the crosshead speeds in the tested crosshead speed range.

On the applicability of the load separation criterion to acrylonitrile/butadiene/styrene terpolymer resins

Load separation constitutes the basis for the experimental evaluation of the J-integral by using the single-specimen technique. The objective of this present paper is to investigate the applicability of the load separation criterion for evaluating the ductile fracture mechanics parameters of acrylonitrile/butadiene/styrene (ABS) terpolymers. This criterion allows the load to be represented as the product of two separate functions, namely a material deformation function and a crack geometry function. Load separation implies a method for J-integral evaluation by using only a single load—displacement measurement. The original method for evaluating J used an energy-rate interpretation, which required several load-displacement measurements to be made for identical specimens with varying crack lengths. J methodology based on load separation introduces new parameters, i.e. η, η e1 and η p1, which greatly simplify the calculation of J and constitute the basis for the J−R multiple specimen technique. Recently, a method for both the experimental determination of the η-factors and the verification of load separation, which is based on separation constants, has been proposed for the testing of steel. This method allows the calibration of the η-factors in new test specimen geometries. This present paper attempts to evaluate experimentally whether the principle of load separation is valid when testing ABS polymers in a bending configuration in order to obtain a valid single J-testing method, and to calculate the η plastic factor experimentally by using this new simple method based on the load separation criterion in non-growing-crack measurements. In addition, a new approach based on the load separation principle which allows not only the calculation of J from a single specimen, but also the calculation of J–R curves from one test measurement has recently appeared. This approach is called the ‘normalization method’ and has already been applied to the J-testing of two rubber-toughened nylons and one ABS polymer. However, load separation has only demonstrated for different specimen geometries in steels. In addition, the load separation in ABS terpolymers has been verified in this present paper for growing cracks, by using an experimental procedure available in the literature.

Study of the load-separation principle and a procedure to estimate ?p-factor for structures with different geometries

The theoretical background of ‘load separation principle’ has been reviewed. Based on dimensional analysis, experimental results and finite element analysis the conditions for the validity of this principle have been studied and a method has been suggested to estimate the load separation function, and hence to estimate the ηp-factor and to determine the J-R resistance curve easily from records of a single specimen or structure.