Biaxial Test Method Research Articles

New developments of formability evaluation methods for hot stamping

Formability is an essential material property that needs to be considered when selecting materials for hot stamping applications. Due to the difficulties of achieving rapid cooling before deformation and the failure of lubricant systems, however, it is challenging to use conventional Nakajima and Marciniak tests to evaluate the formability of materials under hot stamping conditions. Recently, biaxial test methods have shown great potential to overcome this challenge. In this paper, recent developments of the biaxial test methods for formability evaluation are reviewed, including testing machines, specimen designs, specimen heating methods, testing procedures, and limit strain determination methods. Compared to the Nakajima or the Marciniak tests, the biaxial test method can provide better simulation for hot stamping conditions and it can be a promising method for evaluating the formability of sheet metals under hot stamping conditions. However, more developments such as the standardisation of the specimen designs and the limit strain determination methods, are still needed for the wide use of the biaxial test method.

Experimental studies of necking and fracture limits of boron steel sheet under hot stamping conditions

Boron steel is the most widely used material in hot stamping applications for forming automotive body panels with complex shapes and ultra-high strength. Due to the high austenitic transformation temperatures and the complex thermal cycle required for hot stamping, however, it is difficult to evaluate the formability of the material using standard punch test methods developed for room-temperature testing. In this study, a high-temperature modification of a recently developed biaxial test method has been used to determine, in a single test procedure and for the first time, forming limit curves (FLCs) and fracture forming limit curves (FFLCs) for 22MnB5 boron steel sheet with a thickness of 1.5 mm under thermal conditions that are representative of industrial hot stamping processes. A direct resistance heating strategy has been developed, and a recently proposed cruciform specimen design has been modified for high-temperature use. For tests with target temperatures in the range of 750 to 925 °C, the resulting test specimens had the highest temperature at the specimen centre and a temperature difference of less than 45 °C in the gauge area and fracture occurred close to the centre of this area under all test conditions investigated. Limit strains at the onset of necking and at fracture for the material have been determined by applying digital image correlation (DIC) to obtain full-field strain measurements, providing an experimental foundation for constructing both FLCs and FFLCs for industrial applications.

Biaxial test method for determination of FLCs and FFLCs for sheet metals: validation against standard Nakajima method

Recently, a biaxial test method comprising a cruciform specimen design and spatio-temporal method to determine the limit strains has been proposed for the determination of forming limit curves (FLCs) and fracture forming limit curves (FFLCs) for sheet metals. However, this test method has not yet been validated against the existing standard methods. In the present work, this biaxial test method has been applied to the aluminium alloy AA5754 for formability evaluation at room temperature and results from the biaxial test method have been compared with those from the standard Nakajima method. Theoretical analysis has been carried out to compare equi-biaxial tension cases for the two methods; a similar variation of thickness strain with radial distance normalised by the radius of the gauge area is found between the two methods. In the biaxial tests, decreasing the radius of the through-thickness dome profile, with which the gauge area is thinned, leads to fracture nearer the specimen centre but produces a less uniform strain distribution. Importantly, the major strains at necking on the FLC, as determined using the biaxial and the standard test methods, are almost the same in the plane-strain state, while in other strain states, the major strains are slightly lower for the biaxial method than that for the Nakajima method. An FFLC for AA5754 has also been determined using the biaxial test method, in which the major strain at fracture decreases with increasing strain ratio β from −0.5 to 0, while it changes only slightly when β > 0.

The split Hopkinson bar bulge setup: a novel dynamic biaxial test method

In sheet metal forming, very often, large plastic deformations are imposed to a thin plate. An accurate description of the material’s elastoplastic response is therefore of paramount importance to perform finite element (FE) simulations of an actual forming operation. Reliable stressstrain data till significantly larger strains compared to tensile tests can be identified by means of bulge test. In this work, a dynamic hydraulic bulge test is proposed. The novel split Hopkinson bar bulge setup, combines features of classical split Hopkinson pressure bar (SHPB) and hydraulic bulge tests. The special configuration of the Hopkinson bars leaves the sample surface fully accessible. As such, high-speed optical measurements can be performed on the sample surface allowing the application of, for instance, digital image correlation (DIC) for full-field displacement strain mapping. The potential of the facility is explored by performing experiments on 0.8mm thick Al2024-T3 sheet.

A new technique for characterising mechanical properties of materials under hot stamping conditions

In order to characterise mechanical properties of materials (e.g. formability) under hot stamping conditions, significant efforts have been made to the development of the biaxial tensile testing method using cruciform specimens. However, no method for necking strain determination and no cruciform specimen design have been widely accepted. In this study, a new technique for characterising mechanical behaviour of materials under hot stamping conditions has been proposed. It includes two main parts: 1) a novel spatio-temporal method for determining necking and fracture strains, and 2) a cruciform specimen design for formability evaluation using biaxial testing method. In the first part, the theoretical base of the novel spatio-temporal method has been discussed, and the method has been validated by applying to uniaxial tensile tests on AA6082 specimens. The method has also been compared with several existing popular methods, in the determination of limit strain at onset of localised necking. It is found that the novel method has greater simplicity, stability and accuracy for the determination of localised necking strain. In the second part, a proposed cruciform specimen of AA5754 has been tested under the equi-biaxial tension, and both the necking initiation location and the strain path at the location where necking initiates, have been analysed. Furthermore, the novel spatio-temporal method has been applied to the biaxial tensile test for the determination of necking and fracture strains. The results show that the designed cruciform specimen enables to initiate fracture at the centre of the specimen and realisation of linear strain path under equi-biaxial tension.

Determining the Damage and Failure Behaviour of Textile Reinforced Composites under Combined In-Plane and Out-of-Plane Loading.

The absence of sufficient knowledge of the heterogeneous damage behaviour of textile reinforced composites, especially under combined in-plane and out-of-plane loadings, requires the development of multi-scale experimental and numerical methods. In the scope of this paper, three different types of plain weave fabrics with increasing areal weight were considered to characterise the influence of ondulation and nesting effects on the damage behaviour. Therefore an advanced new biaxial testing method has been elaborated to experimentally determine the fracture resistance at the combined biaxial loads. Methods in image processing of the acquired in-situ CT data and micrographs have been utilised to obtain profound knowledge of the textile geometry and the distribution of the fibre volume content of each type. Combining the derived data of the idealised geometry with a numerical multi-scale approach was sufficient to determine the fracture resistances of predefined uniaxial and biaxial load paths. Thereby, Cuntze’s three-dimensional failure mode concept was incorporated to predict damage and failure. The embedded element method was used to obtain a structured mesh of the complex textile geometries. The usage of statistical and visualisation methods contributed to a profound comprehension of the ondulation and nesting effects.

Random generation of the meso-structure of a soil-rock mixture and its application in the study of the mechanical behavior in a landslide dam

A discrete element method (DEM) numerical simulation is used as a tool to study the mechanical behavior of soil-rock mixtures (S-RM) in a landslide dam. A 2D random generation program (R-SRM2D) of the meso-structure of (S-RM) based on random polygonal rock blocks has been developed, and is used to generate the (S-RM) numerical model of the study area. A new multi-circle representation method of polygonal blocks has been developed, which can better model the mechanical properties and failure process of rock blocks. A DEM biaxial test method with a flexible confining stress boundary has also been developed, which can better model the side boundary conditions of the sample. The meso-parameters of the circular particles representing the soil and rock blocks of the (S-RM) have been obtained from laboratory tests and DEM numerical simulations of soil and rock samples. Based on the meso-parameters, a series of biaxial tests of (S-RM) sample have been conducted using the DEM numerical method. The shear strength, failure process and formation mechanism of shear zones in (S-RM) have been studied. With the increase of the confining stress, the rock blocks in or near the shear zones will be broken, changing the shape of the shear zones, and leads to the shear strength of the (S-RM) sample showing nonlinear characteristics. Furthermore, the strength envelope of (S-RM) sample can be fitted through a power law function in the p-q plane.

Investigating the flexural resistance of fiber reinforced cementitious composites under biaxial condition

The flexural resistance of fiber reinforced cementitious composites (FRCCs) under biaxial condition was investigated by using two different types of biaxial bending test methods: the biaxial flexural test (BFT) and the centrally loaded round panel test (RPT). The flexural responses of FRCCs under biaxial condition were then compared with those of FRCCs under uniaxial condition; i.e. four-points bending test (4PBT). The test results, including the equivalent biaxial strength and normalized energy absorption capacity of the RPT, were found to be clearly higher than those of the BFT, and completely different cracking behavior was observed between the two biaxial test methods; the BFT generated numerous randomly distributed micro-cracks at the bottom of specimens, whereas the RPT mostly showed three major cracks, with minor radial cracks around them. In addition, the equivalent flexural tensile strength and normalized energy absorption capacity of the FRCCs under biaxial condition were found to be higher than those under uniaxial condition. The energy absorption capacity and the ratio of flexural tensile strength to the direct tensile strength of FRCCs are dependent on the stress state.

Microscopic investigation of tow geometry changes in a woven prepreg material during draping and consolidation

Changes in tow geometry are measured during draping and consolidation of a helmet component with 5-harness satin weave carbon fibre reinforced plastic (CFRP) prepreg. The tow microstructure is found by sectioning specimens cut from the helmet. Various tow geometry parameters are extracted using image analysis. Results are compared with similar measurements on dry fabric specimens sheared using the bias extension and biaxial test methods [Compos. Sci. Technol. 63 (2003) 99], and on unsheared specimens cured under light pressure or in an autoclave. Results suggest that, for this particular material and process route, the significant differences observed in tow geometry over the surface of the helmet are mainly due to differences in contact pressure between the prepreg and the mould, with the effect of shear deformation less significant. Differences between tows running longitudinal and transverse to the axis of the helmet are ascribed to differences in contact conditions between these sets of tows and the mould surface.

Evaluation Method for Mechanical Property of Bellows Type Air Spring Made of Woven Fabric Reinforced Rubber.

The stress state on the membrane of bellows type air springs made of woven fabric reinforced rubber is bi-axial when they are pressurized. The material properties for a numerical calculation are needed to use the value examined by bi-axial tensile test. It is very difficult to carry out the bi-axial tensile test because of the problem of making specimens or the way of restraining specimens. Therefore, we have proposed a simplified bi-axial testing method in order to obtain the mechanical properties under bi-axial stress state and presented a database of the material properties by this testing method. Moreover we have calculated the transverse spring constants of the bellows type air springs by nonlinear finite element analysis using this database. These results showed good agreements with the experimental results.

Biaxial Test Method for Characterization of Fabric-Film Laminates Used in Scientific Balloons

Space Structures that require lightweight materials with sufficiently high strength and environmental endurance have been in increasing demand since the early 1980’s. However, the biaxial behavior of these structural materials under pressurized loading is rarely found in the literature. An experimental investigation was conducted to develop a test method and hardware to characterize the biaxial behavior of a fabric-film laminate intended for use as a structural envelope for large balloons. The material tested is a composite laminate of three layers. The three layers are: polyester-based woven fabric, 6 microns film of polyester (Mylar type A) and 6 microns film of linear low density polyethylene (LLDPE). The laminate structure provides high strength to weight ratio. In this study, a test technique has been developed to measure the biaxial response of the material to known stress ratios. The information gained from the test can be manipulated to estimate Poisson’s ratio and the development of a material structural model.

Nonlinear Analysis of Woven Fabric-Reinforced Graphite/PMR-15 Composites under Shear-Dominated Biaxial Loads

An elastic-plastic, time-independent, macroscopic, homogenous model of an 8HS woven graphite/PMR-15 composite material has been developed that predicts the nonlinear response of the material subjected to shear-dominated biaxial loads. The model has been used to determine the response of woven composite off-axis and Iosipescu test specimens in nonlinear finite element analyses using a multilinear averaging technique. The numerically calculated response of the specimen was then compared to experimentally obtained data. It has been shown that the numerically calculated stress - strain diagrams of the off-axis specimens are very close to the experimentally obtained curves. It has also been shown that the numerically determined shear stress - strain and load-displacement curves of the woven Iosipescu specimens are close to the experimentally obtained curves up to the point of significant interlaminar damage initiation and propagation. The results obtained in this study clearly demonstrate that the nonlinear material behavior of the graphite/polyimide woven composites subjected to shear-dominated biaxial loading conditions cannot be ignored and should be considered in any stress analysis. The linear-elastic approach grossly overestimates the loads and stresses at failure of these materials in the off-axis and Iosipescu tests. It can be assumed that the same discrepancies will arise in the numerical analysis of the woven composites tested under other biaxial shear-dominated loading conditions using other biaxial test methods.

Biaxial testing of high strength carbon fiber composite cylinders for pulsed magnet reinforcement

Abstract A methodology is introduced to test carbon-fiber-reinforced, hoop-wound composite cylinders for their biaxial mechanical properties under axial compression and hoop tension. The understanding of the behavior of these composites under biaxial loads is extremely important in the design of pulsed magnets. These composites are used as reinforcements for both the inner conducting layers and as an overall exterior reinforcement. Testing of actual pulsed magnets to ascertain design change effects of composite reinforcement schemes on the maximum attainable field can be expensive; hence, a standard biaxial testing method is desirable which is relevant to the design of pulsed magnets. In this investigation, an attempt was made to produce a standard testing procedure aimed at measuring the biaxial mechanical properties (elastic, plastic, and failure envelope) of composite materials. This methodology was applied to two different carbon/epoxy based composites. The results of these tests (elastic properties and failure points) are compared with theoretical predictions, specifically those due to Tsai-Wu.

A biaxial thermomechanical disk test for glassy polymers

Failure criteria for polymers need to include effects from the stress state. For this reason, biaxial test results are of interest. However, biaxial test methods usually require expensive equipment. In the test method presented here, a disk of epoxy is bonded between a steel ring and a steel disk. The temperature is then lowered until fracture is observed. Experiments were performed on three different glassy epoxy polymers. The biaxial stress state was analyzed by finite element analysis and by an approximate analytical model. Experimental observations support the ability of the method to provide material property data. An approximate analytical model was found sufficiently accurate for stress analysis and determination of the stress state at failure.

Lamb wave tomography of advanced composite laminates containing damage

Ultrasonic techniques have been used to image damaged regions in two polymer composite plate samples. The two thin laminate samples studied consisted of 16 layers of carbon-fibre reinforced epoxy with a quasi-isotropic lay-up configuration and had been previously loaded in a biaxial test method until failure. The resulting damage, in the form of fibre failure, matrix cracking and delamination, has been imaged using a novel Lamb wave immersion tomography technique. Images created with this method were correlated with images obtained from C-scan techniques. Both C-scans and Lamb wave tomography were able to identify clearly regions of damage in the two samples.

A comparative study between two rock stress measurement techniques at Luossavaara Mine

As part of a comprehensive geomechanical pre-investigation scheme, rock stress measurements were conducted at four locations, representing three different rock types, in the Luossavaara Mine, located within the Kiruna iron ore fields in northern Sweden. Two similar triaxial overcoring techniques, the CSIRO Hollow Inclusion Technique and the LUH Triaxial Technique, were used in a parallel fashion in order to obtain redundant results, but also with the intention of comparing the field applicability of the two methods. The results show that the state of stress is characterized by a sub-horizontally directed maximum stress with a magnitude of about 10 MPa. The agreement in terms of stress results between the two methods was generally good. The study demonstrated that the technical differences between the two devices used were of little significance as compared to the observed, often non-ideal mechanical characteristics of the rock. The latter added considerable uncertainty to the data, regardless of the measuring technique used, and it is therefore concluded that the rock quality is a major factor in the application of any overcoring method. Finally, it was shown that the biaxial test method, which is frequently used for the determination of rock properties in connection with stress measurements, is not always relevant for this purpose.

Biaxial Test Method for Characterization of Fabric Materials Used in Permanent Fabric Roof Structures

Abstract An experimental investigation was conducted to develop a test method and hardware for the purpose of characterizing the material behavior of coated glass fabrics for application in large roof structures. Because of the biaxial nature of stresses in fabric structures, an internally pressurized cylinder specimen was designed for use in a hydraulically actuated (MTS) testing machine. Biaxial cylinder fabrication and appropriate testing procedures were developed. Stress-strain and strength characteristics were determined for various fabric material types and material lots. Biaxial monotonic, step loading, stress rupture, and dynamic fatigue loading conditions were studied. Combined biaxial tensile plus shear loading were assessed by testing cylinders under biaxial and superimposed torsion loading conditions. The strength characteristics of damaged fabric materials were also extensively assessed.