This paper describes results of post-test analysis of NESC-IV tests conducted on the cruciform clad specimens of type A533 Grade B steel. A total of six clad cruciform specimens containing shallow surface flaws were tested in the temperature interval –55 up to -33 within the transition region of the material. Detailed 3-D elastic-plastic finite element calculations are used to evaluate the outcomes of the test program. Crack driving forces expressed in the J-integral and crack-tip constraint expressed in the Q-parameter are calculated along the whole crack front in the cruciform tests under **biaxial** **loading**. The “Master Curve” methodology is used to predict the experimental outcomes of these experiments. It is observed that the fracture initiated in a region close to the cladding HAZ, where a combination of the crack driving force and the crack-tip constraint is critical. Size-corrected Master Curves predicted reasonably well the fracture events in these experiments. KEYWORDS: clad cruciform specimen, **biaxial** **loading**, finite element calculation, transferability, A533 steel, Q- parameter, master curve

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The experimental studies on the specimens made of artificial geomaterials with structural inhomogeneity in the form of inclusions have allowed the detailed testing of the peculiarities of distribution and evolution of their mi- crolevel stress–strain state on work surfaces of the rock specimens under uniaxial and **biaxial** **loading** to failure using speckle photography method. Within the limits of the experimental study of wave processes in the geome- dia with structural hierarchy of blocks, the earlier found phenomenon of low-frequency microdeformation gen- erated by slow (quasistatic) force has been confirmed.

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A simplified technique for determining the shakedown limit load of a structure was previously developed and successfully applied to benchmark shakedown problems involving uniaxial states of stress [1]. In this paper, the simplified technique is further developed to handle cyclic **biaxial** **loading** resulting in multi-axial states of stress within the plate. Two material models are adopted namely: an elastic-linear strain hardening material model obeying the kinematic hardening (KH) rule and an elastic-perfectly-plastic (EPP) material model. The simplified technique utilizes the finite element (FE) method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full elastic-plastic cyclic **loading** FE simulations or conventional iterative elastic techniques. The simplified technique is utilized to generate the shakedown domain for the problem of a large square plate with a small central hole subjected to cyclic **biaxial** tension along its edges. The outcomes of the simplified technique showed very good correlation with the results of analytical solutions as well as full elastic-plastic cyclic **loading** FE simulations. Material hardening showed no effect on the shakedown limit load of the plate in comparison to employing EPP material.

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3. MAKING OF COLUMN TESTING FRAME Hence in order to apply uniaxial/**biaxial** a self - straining **loading** frame of 25 Tons capacityunder **biaxial** load for column testing has been conceptualized, fabricated and erected. The basic configuration of the **loading** frame consists of seven vertical steel box sections with two hexagonal shape box beam sections with two hexagonal shape box beam sections including cross beams is fixed rigidly to the top and bottom of the vertical members. The horizontal platform by the steel plate of 12mm thick is welded in the both top and bottom at the inner side of the frame and the applied **loading** point at the cross section of the column under **biaxial** **loading**. The maintenance department of SRM University has been carried out Fabrication and erection.

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In previous work, the authors presented a two-dimensional crack initiation and propagation analysis [17]. The computational results were validated by means of comparison with experimental results. In this paper, the main objective is focused in the calculation of SIFs for the real cruciforms submitted to **biaxial** **loading** as well as quantify the edge effects into each geometry. For making that possible, previous computational tests are needed. It is important to notice that in this work a 3D model is simulated. This model has not been validated before and higher numerical complexity is expected compare with the 2D case. Therefore, in Section 4.1 crack initiation and propagation is simulated within the 3D cruciform and compared with experimental outcomes. By means of this first computational analysis the three-dimensional abilities of XFEM are demonstrated. With the confidence of this analysis, the authors are able to go further when dealing with a 3D model. In Section 4.2, a 3D static crack analysis is carried out. This section can be divided into two main parts. The first part, Section 4.2.1, considers a quasi-infinite plate subjected to **biaxial** **loading**. Those plates are equivalent to the central zone of the cruciforms and SIFs are obtained using XFEM and afterwards compared with the theoretical solution. This analysis serves to show that XFEM is capable of accurately obtain SIFs in a **biaxial** **loading** context. The second part, Section 4.2, it is focused in the calculation of SIFs within cruciform specimens once the capabilities of XFEM has been validated in previous sections.

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NESC VII – a European project dealing with WPS based on in-kind contributions – has been launched in 2008 with a wide international participation (17 partners). Based on experimental, analytical and numerical work, the project is focused on topics not covered by past experience and knowledge on WPS : **biaxial** **loading**, effect of irradiation, applicability to different modes of failure, modeling …

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The J -integral solution was derived to determine elastic fracture toughness for ductile metal plates with inclined surface cracks under **biaxial** **loading**. The derived elastic fracture toughness is a function of plate and crack geometry, strain-hardening coefficient, yield strength, fracture toughness, biaxiality ratio, and inclination angle. Parametric studies have shown that an increase in yield strength or relative crack depth, or a decrease in Mode-I fracture toughness, leads to greater relative elastic fracture toughness. It has also been shown that the effect of biaxiality ratio and inclina- tion angle on elastic fracture toughness is highly dependent on total fracture toughness values, which highlights the need for accurate experimental determination of total fracture toughness taking into account the effect of **biaxial** and mixed-mode loadings. It can be concluded that the developed elastic fracture toughness model en- ables engineers and asset managers to accurately predict fracture failure of ductile thin metal structures with inclined cracks under **biaxial** **loading**.

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In this section, the results from simulations are compared with the experimental tests in order to validate the proposed numerical approach for a **biaxial** **loading** context. Several simulations (Table 2) have been performed with three different geometries and **loading** conditions. Experimental results for geometry A are presented in Fig. 5. In that figure, the macro-crack is initiated in the rounded zone and propagated throughout the central zone. The same pattern of failure is observed during experiments for geometries B and C under its corresponding **biaxial** **loading** cases shown on Table 2. The CGRP composite owns random fibre distri- bution within the matrix so any crack observed will consequently provoke matrix cracking and fibre rupture. Due to the manufacture process, the composite is homogeneous through the thickness as Fig. 3. FE mesh of 1/8 of the geometries A–C respectively. Notice a finer mesh in the central zone (0.4 mm) than in the arms (1.4 mm).

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Hence in order to apply Uniaxial/**Biaxial** a self- straining **loading** frame of 25Tons capacity under **biaxial** load for column testing shown in Figure-5 has been conceptualized, fabricated and erected. The basic configuration of the **loading** frame consist of seven vertical Steel box sections with two hexagonal shape box beam sections including cross beams is fixed rigidly to the top and bottom of the vertical members. The horizontal platform by the steel plate of 12mm thick is welded in the both top and bottom at the inner side of the frame and the applied **loading** point at the cross section of the column under **biaxial** **loading** is shown in Figure-1. The

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Tests on plates were carried out by Wright et al., (1994) who found that a **biaxial** **loading** of approximately 0.5 times the uniaxial **loading** increased the fracture toughness; tests on pipes by Østby and Hellesvik (2008) found that a **biaxial** load increased the crack driving force. Cruciform tests enable **biaxial** **loading** to be well controlled but are rare due to the large amount of material required and expensive testing equipment. However, some large-scale tests were carried out for the US Nuclear Regulatory Commission (NRC) at the Oak Ridge National Laboratory, (McAfee, et al., 1995), (Bass et al., 1999), where it was found that **biaxial** **loading** in the form of an additional out-of-plane stress component had the effect of reducing the fracture toughness.

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In this paper, reference stress solutions for plates with semi-elliptical surface cracks were firstly reviewed, and the applicability of the solutions was examined through the comparison with finite element analysis results under uniaxial **loading**. Next, an extended reference stress method was newly developed to evaluate J-integral for cracked plates under **biaxial** **loading**. The predictive accuracy of the method was validated through the comparison with finite element analysis results under **biaxial** **loading**.

Steel plates in concrete-filled thin-walled steel tubular columns under **biaxial** **loading** are subjected to stress gradients. This paper studies the post-local buckling strengths of steel plates under edge stress gradients in concrete-filled steel box beam-columns by using the geometric and material nonlinear finite element analyses. Based on the results obtained from the nonlinear finite element analyses, a set of effective width formulas are proposed for determining the ultimate strengths of steel plates in concrete-filled steel box beam-columns. The proposed design formulas are examined against available design formulas reported in the literature.

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We present an interpretation of the equibiaxial fatigue tests with the definition of the equivalent strain used in the nuclear industry. This is an important step to evaluate the impact of an equibiaxial **loading** on the fatigue life. All tests performed in this study are carried out with imposed displacement (strain) with alternating load (without mean stress or strain), means with a stress ratio R=-1.

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Abstract. It has been proved that plastic instabilities in **biaxial** stretching conditions were better reproduced by using a Tresca yield surface rather than a Von Mises one. The simulation of the phenomenon in an expanding TA6V4 (Ti-6Al-4V alloy) shell experiment is performed using the Tresca criterion and both elasto-plastic and viscoplastic constitutive models: in this aim, Tresca flow surfaces had to be defined in viscoplasticity. The two models exhibit localization but, whereas the elastoplastic case develops shear banding in times in agreement with the onset of instabilities in the experiment, the viscoplastic case develops di ﬀ use necking at later times. On the contrary, the viscoplastic simulation exhibits patterns the size of which seems in better agreement with the experimental ones.

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Two types of stress-strain relations were prepared. One was the elastic-perfectly plastic stress-strain relation, whose results were used to validate the proposed limit moment solution under **biaxial** **loading**, and the other was elastic-plastic stress-strain relation, whose results were applied to validate the proposed J- evaluation method under **biaxial** **loading**. Table 2 shows the material properties used in the analyses. For the elastic-plastic analysis, J-integrals both at the deepest points and at the surface points were evaluated by path-integrals. Fig. 3 shows an example of finite element mesh.

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Figure 3a shows the strain measured by the gauges as function of time. After time shifting to virtually trans- port the signals from the strain gauges to the multi-axial set-up interfaces, and after Hopkinson formulae applica- tion, we can plot the forces and the velocities at these in- terfaces (figures 3b and 3c). During the steady state, all velocities are equal, and the forces applied by the inci- dent and the transmitted bars are equal too. In our case, we have to compare the incident bar force to the sum of the two transmission bars forces to check at the equi- librium [6]. These requirements are confirmed in figure 3c. However we observe that force in the internal trans- mitter bar is a few lower than the force in the external transmitter bar denoting that **biaxial** **loading** is not per- fectly equiproportional. This di ff erence can be explained by a friction in the **biaxial** set up, higher along x direc- tion than along y direction. Average stress components σ xx and σ yy are calculated form forces thanks to equa-

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Abstract: This paper presents an investigation of different cruciform specimen designs for the characterization of sheet molding compound (SMC) under **biaxial** **loading**. The considered material is a discontinuous glass fiber reinforced thermoset. We define various (material-specific) requirements for an optimal specimen design. One key challenge represents the achievement of a high strain level in the center region of the cruciform specimen in order to observe damage, at the same time prevention of premature failure in the clamped specimen arms. Starting from the ISO norm for sheet metals, we introduce design variations, including two concepts to reinforce the specimens’ arms. An experimental evaluation includes two different **loading** scenarios, uniaxial tension and equi-**biaxial** tension. The best fit in terms of the defined optimality criteria, is a specimen manufactured in a layup with unidirectional reinforcing outer layers where a gentle milling process exposed the pure SMC in the center region of the specimen. This specimen performed superior for all considered **loading** conditions, for instance, in the uniaxial **loading** scenario, the average strain in the center region reached 87% of the failure strain in a uniaxial tensile bone specimen.

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Figure-9 shows a typical axial load-displacement curves (for specimens under **biaxial** **loading**) when the specimens were arranged with their axes in the vertical and horizontal direction, respectively, along with the mean curves. The collapse load and energy absorbed shown for both cases are about 15 kN (Figure-9) and 300 Nm, respectively. Overall, their behaviours in both cases are also repeatable. Two view of a typical deformed (cell axes were horizontal in this case) is shown in Figure-10.

It is generally accepted that concrete under cyclic **loading** loses its strength gradually with an increase in the number of load cycles regardless of the **loading** path (uniaxial or **biaxial**). The strength loss during the fatigue process is due to nucleation and propagation of microcracks. During cyclic **loading**, these microcracks increase and grow to a stage in which major cracks are formed and reduce the load carrying area tremendously. At that point the strength of the material is decreased substantially and approaches the amplitude of the cyclic **loading**. This results in sudden rupture. It has been argued that at any given cycle, the fatigue strength of concrete under **biaxial** compression is greater than that under uniaxial compression [12] [14]. This is the result of the relative confinement provided in the **biaxial** **loading** state. This confinement restricts the nucleation and propagation of microcracks by applying load in two perpendicular directions.

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number of actuators employed has direct impact on the numbers of components (sensors, motors, ball runner blocks, linear guides, cables, connectors, input/output electronic channels. Due to the reduced market for this equipment there is no standard and each testing rig is the result of a unique project developed by the supplier according to the requirements of the client. A cost analysis carried out for the development of the **biaxial** testing machine at clusTEX testing laboratory highlighted that the commercial value for the equipment (testing machine + controlling software) can be estimated equal to: 60k€ for a “floating frame” concept (central area 50cmx50cm), 150 k€ for a “symmetric **loading**” concept (70cmx70cm), and 320k€ for a “square frame with batteries of independent servomotors” concept (70cmx70cm). The main part of the costs is related to the selling margins, the engineering costs and the development of the controlling software. When the equipment and the software is developed internally by the research centre/university the costs can be reduced considerably (40- 50%).

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