Uniaxial Bending Research Articles

A Case Study on the Possibility of Extending the Service Life of the Demining Machine Belt.

The operational practice of the design of the Bozena 5 demining machine has shown that its belts are the critical component that fundamentally affects the functionality of the entire machine. This article is a practical continuation and extension of the previous research results from the point of view of materials (research of the uniaxial fatigue life in bending and torsion), calculation (creation of the necessary mathematical, analytical and numerical models for the research) and construction (i.e., patented design of the belt tensioning of this machine). All these actions are aimed at a single objective-to achieve a condition that guarantees a sufficient service life without malfunctions, since repairing these machines in the field is often impossible. Therefore, this study examined the fatigue life of welded joints (uniaxial bending and torsion) of S960 QL and S500MC steels welded by MAG technology. Subsequently, the data were compared with previous results (electron and laser welds) and the influence of each type of weld on the fatigue life relative to the base material was discussed. It was found that conventional MAG technology had a more significant negative impact on the fatigue life of the base material than non-conventional technologies. This trend was particularly true for the bending stress. At the same time, the bending stress was identified by the FEM analysis as the dominant load on the belt. The maximum stress in the belt link under the considered boundary conditions was approximately 240 MPa (in bending). This stress corresponded to the continuous fatigue life (more than 107 cycles) for both base materials tested (S960QL, S500MC). In the whole studied spectrum of controlled deformation amplitudes (Manson-Coffin), the life of MAG welds was lower in comparison with the base material and with welds made by unconventional technologies. All the activities carried out so far (research on microstructure, hardness, strength, residual stresses, tribological properties and fatigue life) have shown that the original belt design (S500MC) using MAG technology has significant deficiencies in the state of optimal life. It is expected that the proposed material change (use of S960QL instead of S500MC) and work with advanced technologies will bring this state significantly closer.

Comparison of the Torsional Strength of Material Samples Made Using Selected Rapid Prototyping Methods

In recent years, there has been a marked increase in the use of rapid prototyping techniques that support industrial processes. The analysis of studies on strength tests of parts manufactured using additive techniques from model materials and hybrid composites usually includes tests of material and strength parameters based on uniaxial tension, bending, and compression tests. For elements manufactured from polymeric materials using traditional methods (e.g. injection moulding), data obtained from these tests are sufficient to determine the strength of the material and to apply the results in the product design process. In the case of the layered extrusion method, due to the model construction process, strength data based on standard samples do not have a direct transposition on the strength of machine parts operating under various load ranges, especially torsional loads. The publication presents the results of tests on the torsional strength of cylindrical samples with splines produced by layered extrusion, vacuum casting technology, and hybrid technology, which combines both technologies. The test samples were made using a Prusa i3 MK3 3D printer and the plasticised plastic modelling (fused filament fabrication, FFF) method, while PolyJet technology was used to create a reference model. The findings indicate that hybrid technology, in which a thin-walled mould is filled with a chemically hardened polymer, achieves the desired strength for the manufactured parts while maintaining dimensional accuracy and shape. The research results show that producing rotating elements using the hybrid technology reduces the sample core’s ability to undergo plastic deformation due to the adhesion between the materials and the occurrence of notches resulting from the model production process using the layered extrusion method.

A rheological constitutive model to predict the anisotropic biaxial bending behavior of spiral strands subjected to variable axial force

Spiral strands exhibit dissipative bending behavior when subjected to external axial force. To the best of the authors’ knowledge, only the uniaxial bending behavior of spiral strands subjected to constant axial force has been studied in the literature so far. Thanks to a recently developed mixed stress–strain driven computational homogenization for spiral strands, this paper is the first to study the biaxial bending behavior of spiral strands subjected to variable tensile force. Based on the observed anisotropic behavior, a rheological constitutive model equivalent to multilayer spiral strands is proposed to predict their behavior under such loading. For an Nl-layer strand, the proposed model consists of several angularly distributed uniaxial spring systems, referred to as a multiaxial spring system, where each uniaxial spring system consists of a spring and Nl slider-springs. In a uniaxial spring system, the spring represents the slip contribution of all wires to the bending stiffness of the strand, while each slider-spring represents the stick contribution of each layer. A major advantage of the proposed scheme is its straightforward parameter identification, requiring only several monotonic uniaxial bendings under constant axial force. The proposed rheological model has been verified against the responses obtained from the mixed stress–strain driven computational homogenization through several numerical examples. These examples consist of complex uniaxial and biaxial load cases with variable tensile force. It has been shown that the proposed scheme not only predicts the response of the strand, but also provides helpful insight into the complex underlying mechanism of spiral strands. Furthermore, the low computational cost of the proposed models makes them perfect candidates for implementation as a constitutive law in a beam model. Using a single beam with the proposed constitutive law, spiral strand simulations can be performed in a few seconds on a laptop instead of a few hours or days on a supercomputer.

Dimension-reduced mathematical modeling of self-shaping wooden composite bilayers

ABSTRACT Swelling and shrinkage of wood provides challenges when used as construction material. On the positive side, it allows for manufacturing curved wood elements by self-shaping upon drying. We present a two-dimensional model for simulating the moisture-induced bending of wooden bilayers and more general composite plates with multiple, periodically distributed material phases. The model is derived in a mathematically rigorous way from a fully three-dimensional nonlinear hyperelasticity model of the plate and is computationally cheap to handle. We focus specifically on the scenario of free deformations. While the derived model is capable to describe general isometric bending deformations, it has the property that free deformations in equilibrium are given by uniaxial bending deformations that can be computed without the need for solving the plate equations via finite element simulations. The hereby gained computational efficiency enables extensive parameter studies to be conducted regarding the design of wooden composite plates with complex composite geometry. We validate the model for homogeneous wooden bilayers and obtain good agreement between simulations and experimental data. Then we use the model to predict the bending behavior of periodically perforated bilayers. The comparison to other existing models and implications for practical use are discussed.

Flexural behavior of novel marine concrete filled CFRP-aluminum alloy tube member

This study proposes a novel marine concrete filled CFRP-aluminum alloy tube (CFRP-CFAT) member for marine engineering. Six specimens including one marine concrete filled aluminum alloy tube (CFAT) and five CFRP-CFAT specimens were tested under uniaxial bending to investigate the flexural behavior of CFRP-CFAT. The effects of CFRP pasting positions, CFRP layers and shear span ratio were investigated. The failure patterns, mid span deflection curves, distribution of the deflection curves, strain, ultimate moment, ductility, flexural stiffness were analyzed. The experiment results illustrate that the failure pattern of CFAT specimen can be improved by CFRP. With the increase in mid-span deflection, the neutral axis shifts towards the compression zone. CFRP enhances the flexural capacity of CFAT specimens, the enhancement of inner CFRP was slightly better. The shear-span ratio does not have a significant impact on the flexural capacity. Compared to CFAT specimens, the use of CFRP leads to a decrease in ductility due to its brittle fracture. Calculation methods for CFRP-CFAT stiffness and bending moment capacity considering the influence of CFRP were proposed.

Mechanical Flexibility and Electrical Reliability of ZnO-Al Thin Films on Polymer Substrates Under Different External Deformation

Abstract Aluminum-doped zinc oxide (AZO) films have emerged as promising transparent electrodes for various optoelectronic applications due to their superior transparency, electrical conductivity, and cost-effectiveness compared to indium tin oxide (ITO). Despite their widespread use, investigations into the electromechanical properties of AZO films, especially under various mechanical deformations, remain limited. This study employs RF magnetron sputtering to deposit AZO films on polyethylene naphthalate (PEN) substrates and explores their mechanical behavior through uniaxial tensile fragmentation and bending tests, coupled with in-situ optical microscopy. Changes in electrical resistance of AZO films were monitored in situ during deformation. Fatigue behavior was examined to further understand mechanical failure, and SEM was used for surface characterization. A critical strain of about 3.1 percent was detected during uniaxial tensile testing, marking the onset of cracks in AZO-coated PEN. In contrast to thicker films, thinner films demonstrated improved stretchability beyond the initiation of crack onset strain. Tension and compression bending tests revealed that the material has excellent bendability, as shown by its critical radii of 5.4 mm and 3.9 mm, respectively. The bending reliability of AZO films under compression was found to be superior than that under tension. Bending fatigue experiments demonstrated that AZO films could withstand cyclic stress without experiencing no ticeable cracks after 100 cycles and with very minor resistance change. This study contributes to the creation of more reliable and optimized flexible optoelectronic devices by giving substantial quantitative data on the performance of AZO films when exposed to mechanical stress.

Investigational studies of asphalt concrete elastic moduli for pavement design

In recent years in the Russian Federation there has been a significant expansion of road materials variety used on highways. However, there is a lack of harmonization of new asphalt concrete of Western European format, with regulatory documents for the non-rigid pavement design, in terms of their design characteristics assignment. In this regard, there is a need to determine and justify the numerical values of the new asphalt concrete mechanical performance used for the non-rigid pavement design when tested for strength. In previous publications authors have presented a new graph-analytical approach to justify the elasticity design moduli of asphalt concrete from GOST R 58406.2-2020. This paper is a continuation of that development and includes the empirical verification results of the analytical method accuracy. Tests were carried out to determine the static laboratory elasticity modulus of asphalt concrete under uniaxial bending loading of bar specimens of some asphalt concrete types from GOST R 58406.2 and best corresponding ones from GOST 9128. To the values obtained, during the experiment, the calculation method developed by the authors earlier was applied. The article presents a study aimed at experimental confirmation of analytically justified calculated values of asphalt concrete elastic moduli according to GOST R 58406.2-2021 for the pavement design.

GLARE deformation in low-restraint state: Tensile and bending behavior

Fiber metal laminates (FMLs) possess a better weight reduction effect than traditional metal materials due to the coupling properties of heterogeneous materials, showing promise in the areas of aviation and aerospace. At present, the research on FMLs mainly focuses on the deformation properties after curing while the mechanical properties in the low-restraint state, i.e. the laminates are temporarily not cured and are formed under lower constraint stresses, are not studied in detail. Herein, the low-restraint GLARE is taken as a research object and its deformation characteristics and failure mode are studied using uniaxial tensile, bending experiments and numerical simulation in this paper. Moreover, the influence of key parameters, such as temperature, laminate structure and span length, is investigated, as well as the tensile and bending deformation behavior of GLARE in a low-restraint state is obtained. In addition, based on experimental observations, it is found that the low-restraint GLARE produces the phenomenon of interlayer slip, and the interlaminar residual stress is much smaller than the cured laminate, whereas the deformation limit and performance are improved. This paper provides theoretical bases for the in-depth analysis of deformation properties and forming laws of low-restraint GLARE, guiding further applications of laminates.

Study on biaxial bending fatigue performance of Engineered Cementitious Composites (ECC)

Structural components such as bridge deck, highway pavement and thin-walled roof dome often are subjected to the biaxial and even multi-axis stress state due to the external load. Also, the fatigue effect cannot be ignored due to the moving vehicle load in the design of these structures. If engineering cementitious composites (ECC) is used in the above traditional concrete structures, their performance, such as easy cracking and short service life can be greatly improved. However, the biaxial bending fatigue performance of ECC should be analyzed in detail. At present, the biaxial bending test methods of cement-based materials include biaxial bending test (BFT) and centrally loaded round panel test (RPT). This study used both RPT and BFT test methods to analyze the biaxial fatigue performance of ECC and used four-point bending test (4PBT) uniaxial fatigue test as a reference. The stress levels S were set as 0.5, 0.6 and 0.7. The uniaxial and biaxial bending fatigue failure procedures of ECC were analyzed by plotting the three-stage deflection development curve, the fatigue damage and strain relationship curve based on the linear cumulative fatigue damage theory, and the S–N curve. The fatigue life of ECC biaxial bending specimens was greater than that of uniaxial bending specimens. At S = 0.5, the fatigue life: BFT > RPT. At S = 0.6, the fatigue life of BFT and RPT specimens was close. At S = 0.7, the fatigue life: BFT < RPT. With increasing stress level, the fatigue life of BFT specimen decreases more than that of RPT specimen. The lognormal distribution model and Weibull distribution model were used to fit the uniaxial and biaxial bending fatigue life of ECC, respsectively. Using the double logarithmic fatigue equation, fatigue life under the failure probability PF of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 was derived. The survival rate represents the level of safety reservation, which could provide reference and basis for the design of ECC bridge deck and highway pavement with different safety reservation requirements.

Loading protocols for quasi-static cyclic testing of flexure dominated reinforced concrete circular bridge columns under crustal, subcrustal, and subduction earthquakes

Experimental procedures involving quasi-static cyclic tests have been the most prevalent for seismic performance assessments of structural and non-structural components and systems. However, there is a lack of consensus among experimentalists and researchers on a standard loading protocol. This study aims to propose a set of standard loading protocols representative of the seismic demands imposed on typical flexure dominated reinforced concrete bridge columns under uniaxial bending. Variable parameters: axial-load ratio, aspect ratio, longitudinal and spiral reinforcement ratios, concrete compressive strength, and steel yield strength were initially screened for significance in terms of their influence on the number of inelastic cycles and cumulative displacement ductility - two key reference parameters for the development of loading protocols. The number of inelastic cycles cumulative displacement ductility were then determined for reinforced concrete bridge columns having unique combinations of upper and lower levels of the significant parameters under different earthquake types (crustal, subcrustal, subduction) and displacement ductility demand levels (2, 4, 8). These target ductility demands intend to capture a wide range of structural responses including minimal and collapse damage states. Statistical analyses revealed that for the considered bridge columns, it is feasible to develop one representative loading protocol for each earthquake type and target displacement ductility demand level. Hence, nine loading protocols were proposed and then compared against equivalent loading protocols found in standards and literature. Standard protocols were found to impose unrealistic damage on bridge columns subjected to crustal and subcrustal earthquake hazards leading to inaccurate assessments. The proposed loading protocols for subduction earthquakes had a comparable number of inelastic cycles to those found in the literature for the same earthquake hazard and are representative of the seismic demands imposed on bridge columns.

Mechanical Characterization of Bi-Layer Environmental Barrier Coatings Under Tension and Bending Using Acoustic Emission and Digital Image Correlation

Abstract Fracture characteristics of bi-layer environmental barrier coatings (EBC) deposited on a woven ceramic matrix composite (CMC) substrate using air plasma spray processes were investigated under uni-axial tension and bend tests at room temperature. Health monitoring techniques such as acoustic emission (AE) and digital image correlation (DIC) were employed to better understand the cracking behavior of the coating and its progression. Post-test microscopy was performed to correlate the coating cracks with DIC and AE location. The results indicate that multiple transverse cracks first occurred in the coating, followed by substrate transverse cracks and additional coating cracks. DIC analysis was able to highlight the formation and location of these cracks. The fracture strength of the coating was estimated assuming the composite beam theory.

Fiber–Based Model for Simulating Inelastic Interaction Buckling of Rectangular CFST Slender Columns with Unequal Wall Thickness

Rectangular concrete-filled steel tubular (RCFST) columns can be designed to have unequal wall thickness to maximize their resistance to combined axial and uniaxial bending loads. However, there is very little published research on their local–global interaction buckling behavior. This paper presents an efficient fiber-based simulation model for analyzing the inelastic interaction buckling of eccentrically loaded RCFST slender columns with unequal wall thickness. The model considers the progressive local–global interaction buckling, distributed plasticity, concrete cracking and crushing, second-order effects, and geometric imperfections. The mathematical model is programmed to compute not only the axial load–displacement responses but also the interaction curves of axial load and moment of slender RCFST columns. The simulation modeling is validated by experimentally measured data. The validated computer model is used to parametrically study the interaction local–global buckling responses of RCFST columns while the range analysis is conducted to identify the relative significance of key parameters. It is demonstrated that the proposed computer model accurately simulates experimentally measured responses. Hence, it can be used with confidence in practice to analyze and design RCFST slender columns fabricated with steel plates of unequal thickness. The existing design standard AS/NZS 2327:2017 provides acceptable strength predictions of RCFST slender columns and beam-columns while the procedure specified in Eurocode 4 overestimates their capacities.

Experimental investigation of wrapped composite X‐joints under uniaxial and multi‐axial loading conditions

AbstractCircular hollow section (CHS) multi‐membered structures, such as off‐shore wind turbine jackets and floating wind structures, face significant challenges under multiaxial loads. Wrapped composite joints have emerged as a promising alternative to conventional welded joints, offering superior structural and fatigue performance in previous pilot tests. This paper presents an experimental study on the failure mechanisms and load‐bearing capacity of wrapped composite joints under multi‐axial monotonic loading, using the Hexapod a six‐degree‐of‐freedom testing machine. The research question addressed in this study is to investigate the effectiveness of wrapped composite joints in resisting multi‐axial loads, and to understand the underlying failure modes. The experimental results demonstrate that the joints exhibit excellent resistance to uniaxial tension, uniaxial bending, and multi‐axial tension + bending loading, with failure modes including interfacial debonding, delamination, composite fracture, and steel yielding. Digital Image Correlation (DIC) and embedded optical fibers were used to monitor surface and interface strain. These findings suggest that wrapped composite joints offer significant resistance to multi‐axial loading.

Numerical assessment of the cyclic behaviour of structural steel members subjected to biaxial bending

AbstractIn recent decades, there has been extensive research on the behaviour of steel structures under seismic actions. While the monotonic behaviour of steel elements subjected to uniaxial bending is well understood, there is still a need to investigate the cyclic behaviour and energy dissipation capacity, especially in relation to metal elements subjected to biaxial bending. This is of paramount interest for seismic analysis and performance assessment of steel buildings. Modelling and damage assessment criteria derived for members subjected to uniaxial bending may not be entirely appropriate for the seismic analysis of buildings composed of structural steel members subjected to biaxial bending. Therefore, this research aims to investigate the behaviour of steel members subjected to biaxial cyclic bending and compare it to behaviour under uniaxial loading conditions. To this end, detailed 3D finite element analyses are conducted to examine the effects of bidirectional lateral cyclic loading on the hysteretic response of steel members under different uniaxial and biaxial lateral displacement‐controlled load paths. The numerical results presented in this paper provide an insight into the influence of biaxial loading on the behaviour of steel members in terms of backbone curves and deformation capacity, and indicate that biaxial cyclic loading paths can significantly affect the rotation capacity of steel elements.

Stress and strain calculation method for orthotropic polymer composites under axial and bending ultrasonic fatigue loads

Accelerated fatigue testing is one potential solution to evaluate the very high cycle fatigue behavior of composite materials within a reasonable amount of time. The ultrasonic fatigue testing methodology can be adopted to realize fatigue experiments up to 109 cycles at 20 kHz, compared to conventional fatigue experiments usually carried out between 5–50 Hz. The determination of cyclic stresses during ultrasonic loading remains to be one of the major challenges. The cyclic stresses during ultrasonic fatigue loading were investigated for a carbon fiber 5H satin fabric reinforced in Polyetherketoneketone (CF-PEKK) composite material. Two experimental setups were developed to perform ultrasonic testing under uni-axial and three-point bending loading conditions. A 3D-Scanning Laser Doppler Vibrometer (3D-SLDV) and a single-point Laser Doppler Vibrometer (LDV) were integrated into the test systems to measure the oscillation displacement of the CF-PEKK specimens during ultrasonic cyclic loading. These displacement measurements were used to calculate the resulting strains and stresses under elastic loading conditions. The experimental results were found to be in good agreement with those obtained from finite element models, providing evidence for applying the proposed method.

Methodology for strength distribution estimation of ceramics from ball-on-three-balls and four-point bending experiments, Weibull statistics and fractographic investigations: Application to magnesium aluminum spinel

The present paper aims to propose a reliable analysis of ball-on-three-balls and four-point bending experiments applied to advanced ceramics combining statistical analyses, numerical modelling and fractography. MgAl2O4 transparent spinel ceramic was selected to facilitate the assessment of samples quality. Following the material processing procedure detailed in the literature, numerous spinel samples of two different geometries (20 and 60 mm in diameter) were produced. Knoop Hardness and Young's modulus values of 11.8 GPa and 290 GPa were measured, respectively. A three-modal grain size distribution was observed through the sample's thickness. Biaxial bending tests have been performed in conjunction with numerical simulations using Abaqus/Standard®. Thus, parallelism defects were taken into account and their effects on the maximal stress and effective volume were quantified. They were found to be very close to the only published data. In addition, four-point bending experiments were carried out and validated using an ultra-high-speed camera. The scattering of the bending strength was modelled using a two-parameter Weibull distribution and the maximum likelihood approach. 90% confidence intervals of the parameters and confidence bounds of the probability of failure were computed using the likelihood ratio test. This approach is more suitable than Monte Carlo simulations with regard to computational costs. According to the Weibull theory and biaxial bending strength distribution, the material strength, rescaled for different effective volumes was slightly overestimated, in comparison with four-point bending results. Fractographic analyses on uniaxial bending samples revealed that fractures originate from large grains. The corresponding study on biaxial bending samples revealed that carbon inclusions located near to the surface seem to be responsible for failure. Finally, this study brings additional arguments for a more intensive use of the ball-on-three-balls set-up especially when concerns about costs, sample geometry and test practicality are raised.

A robust identification procedure for phase field fracture mechanics parameters

The classical Phase Field (PF) model for fracture mechanics of brittle materials based on the finite element method involves three parameters in addition to the Poisson ratio ν: the Young’s modulus E, the fracture toughness Gc, and the internal length scale lc. The latter is mathematically conceived as a numerical regularization parameter that should tend to zero to recover linear elastic fracture mechanics (LEFM) predictions. To address this issue, a robust algorithm is implemented in MATLAB, which combines Particle Swarm Optimization (PSO) and the Phase Field (PF) approach to fracture based on the finite element method. The algorithm has been applied to a series of uni-axial tensile tests (with E and lc to be identified) and to three-point bending tests (with E, lc and also Gc to be identified) on specimens made of ABS material. Results show that the optimal values of E and Gc are consistent in both tests, while lc presents a significant dependency upon the test type. Therefore, different values of the internal length scale should be identified and used to match the experimental responses under uni-axial tension or bending.

High-temperature fracture behaviour of layered alumina ceramics with textured microstructure

Mimicking the damage tolerance of biological materials such as nacre has been realised in textured layered alumina ceramics, showing improved reliability as well as fracture resistance at room temperature. In this work, the fracture behaviour of alumina ceramics with textured microstructure and laminates with embedded textured layers are investigated under uniaxial bending tests at elevated temperatures (up to 1200°C). At temperatures higher than 800°C monolithic textured alumina favours crack deflection along the basal grain boundaries, corresponding to the transition from brittle to more ductile behaviour. In the case of laminates, the loss of compressive residual stresses is counterbalanced by the textured microstructure, effective up to 1200°C. This study demonstrates the potential of tailoring microstructure and architecture in ceramics to enhance damage tolerance within a wide range of temperatures.

Case studies on determining fire resistance of uniaxial bending reinforced concrete columns subjected to 4-side standard fire exposure

This article introduces technical specifications and calculation instructions for fire resistance of uniaxial bending rectangular reinforced concrete (RC) columns under 4-side heating by standard fire. Although a number ofresearch works have been conducted following the Eurocodes to meet the long-term requirement of the country’s development in construction, it is shown that the Russian design standard SP 468.1325800.2019 (SP 468) is also applicable for concrete structures subjected to fire in the Vietnam current context. Tabulated data and simplified calculation methods according to SP 468 are introduced, followed by two practical case studies for demonstration. The calculation results show that by using the simplified calculation method the RC columns’fire-resistant limit can be explicitly determined with a particular safety factor ku, T, and a more economical design solution can be obtained compared to that of the tabulated data method. Additionally, RC columns loaded with small eccentricities exhibit greater fire resistance advantages compared to those with large-eccentricity loading. A number of other useful observations are also discussed in the latter part of this article.

A novel unified constraint parameter based on plastic strain energy

Constraint, defined as the resistance of a component against plastic deformation, has a significant effect on the materials’ fracture toughness. A loss of constraint can mean a higher fracture toughness. The standard test geometries such as C(T) specimens are designed to have high levels of constraint thus ensuring that a lower bound toughness is measured. To get a more accurate estimate of the integrity of low constraint components, it is necessary to study an approach of quantifying the constraint level and evaluating it on failure load. Currently, widely accepted crack-tip constraint parameters are validated using specimens with uniaxial loading such as C(T) and SEN(B). However, a large number of industrial equipment experiences loading modes other than uniaxial. The multi-axiality has been considered an important effect in various standards. Load multiaxiality can cause a change in constraint thus fracture toughness. In this paper, a novel unified constraint parameter λ based on the plastic strain energy was proposed. A series of uniaxial and biaxial bending experiments made of BS1501-224 28B steel were conducted at −160℃. A large amount of previous fracture test data of C(T) and SEN(B) specimens were used to support the study. The elastic–plastic parameter Q and the unified parameters φ, Ad* were calculated as a comparison. It is shown that the newly suggested parameter λ not only can characterize the constraint of C(T) and SEN(B) specimens but is effective in characterizing the multi-axiality effect while traditional constraint parameters fail to do so.