Biaxial tensile fatigue testing service

Biaxial Tensile Fatigue Testing Service – Accredited ISO/IEC 17025 Multi‑Axial Mechanical Performance Assessment for the Croatian Market

Biaxial tensile fatigue testing is a specialized mechanical characterization method used to evaluate the fatigue behavior of materials and components subjected to simultaneous cyclic loading in two perpendicular directions. This testing is essential for understanding the performance of materials under complex, real‑world stress states that occur in pressure vessels, pipelines, aircraft fuselages, automotive body panels, membrane structures, and composite laminates, where multiaxial loading conditions are prevalent. In the Croatian market, where the Hrvatski zavod za norme (HZN), the Ministarstvo gospodarstva i održivog razvoja, the Državni inspektorat, and the Carinska uprava enforce strict quality, safety, and reliability standards aligned with EU directives and HRN EN (Croatian standards based on European norms), the accurate evaluation of biaxial tensile fatigue resistance is essential for product certification, design validation, supplier qualification, quality control in manufacturing, and import‑export processes. Our laboratory offers a comprehensive biaxial tensile fatigue testing service, applying standardized methods that measure fatigue life, crack initiation, and crack propagation under controlled biaxial stress ratios, phase angles, and loading frequencies, in accordance with ASTM E2207, ISO 1099, and HRN EN ISO 1099. All tests are performed under our ISO/IEC 17025 (CNAS) accreditation, and the resulting reports are fully accepted by Croatian authorities and notified bodies, making them indispensable for regulatory compliance, product validation, and market access in Croatia and the European Union.

Test Samples and Materials We Regularly Examine

Our laboratory receives a wide variety of materials and components for biaxial tensile fatigue testing. Typical samples include:

• Thin sheets and plates – steel, aluminum, titanium, and nickel alloys used in aerospace, automotive, and pressure vessel applications.
• Composite laminates – carbon fiber, glass fiber, and hybrid composites for aerospace, wind energy, and automotive structures.
• Polymer films and membranes – for flexible packaging, inflatable structures, and medical devices.
• Welded and joined assemblies – cruciform and cross‑shaped welded joints for evaluating the fatigue performance of welded connections.
• Prototype and new material formulations – submitted by manufacturers for validation of biaxial fatigue resistance before series production.
• Field‑retrieved components – for failure analysis and remaining life assessment.

Biaxial Fatigue Testing – Cruciform and Tubular Specimen Methods

Biaxial tensile fatigue testing is typically performed using cruciform (cross‑shaped) specimens or tubular specimens, which are subjected to independent cyclic loads in the two principal directions. Our tests follow international standards and the requirements of the Croatian aerospace, automotive, and energy sectors.

• Biaxial fatigue test – cruciform specimen method (ASTM E2207 / NTC 5800 – for thin sheet materials) – we machine a cruciform specimen from the test material, with a reduced‑thickness gauge section in the center. The specimen is mounted in a biaxial testing machine equipped with two independent servo‑hydraulic actuators (or two electromechanical actuators) that apply cyclic loads along the two perpendicular axes (X and Y). The loads are applied at a specified stress ratio (R = σ_min / σ_max), phase angle (φ), and frequency (e.g., 1‑10 Hz). The test is continued until the specimen fails or until a specified number of cycles (e.g., 10⁷ cycles) is reached. We report the fatigue life (cycles), the stress amplitudes (σ_x and σ_y), the stress ratio, the phase angle, and the failure mode.
• Biaxial fatigue test – tubular specimen method (NTC 5801 – for pipes and tubes) – we machine a tubular specimen from the material (or use a section of the pipe) and seal both ends. The specimen is subjected to an internal pressure (which generates a circumferential (hoop) stress) and an axial load (which generates a longitudinal stress), both applied cyclically. The internal pressure is controlled by a hydraulic system, and the axial load is controlled by a servo‑hydraulic actuator. The biaxial stress ratio is determined by the ratio of the hoop stress to the axial stress. We report the fatigue life, the hoop and axial stress amplitudes, and the failure mode.
• Biaxial fatigue test with different phase angles (NTC 5802 – for the effect of the phase shift) – we perform the biaxial fatigue test with different phase angles between the two loading axes (e.g., φ = 0°, 45°, 90°, 135°, 180°). The phase angle determines the shape of the loading cycle (e.g., proportional loading for φ = 0°, out‑of‑phase loading for φ = 90°). We report the fatigue life at each phase angle and the effect of the phase angle.
• Biaxial fatigue test at different stress ratios (NTC 5803 – for the effect of the mean stress) – we perform the biaxial fatigue test with different stress ratios (e.g., R = -1, 0, 0.5) to evaluate the effect of the mean stress on the fatigue life. We report the fatigue life at each stress ratio and the mean stress sensitivity.
• Biaxial fatigue test at different temperatures (NTC 5804 – for the thermal effect on fatigue) – we perform the biaxial fatigue test at elevated temperatures (e.g., 100 °C, 200 °C) or at low temperatures (e.g., -20 °C) using a temperature‑controlled chamber. The effect of temperature on the fatigue life is evaluated. We report the fatigue life at each temperature and the temperature derating factor.

Fatigue Life and S‑N Curve Determination – Predicting the Service Life

The primary result of the biaxial fatigue test is the fatigue life (the number of cycles to failure) at a given stress amplitude. By performing tests at multiple stress amplitudes, we construct the S‑N curve (stress vs. cycles to failure), which is essential for the design of components with a specified service life and for the calculation of the fatigue safety factor.

• S‑N curve determination (ISO 1099 / HRN EN ISO 1099 / NTC 5810 – for the fatigue life estimation) – we perform a series of biaxial fatigue tests at different stress amplitudes (typically 4 to 6 levels) while keeping the stress ratio and the phase angle constant. The number of cycles to failure is recorded for each test. The S‑N curve is plotted on a log‑log scale, and the curve is fitted using a power law (Basquin's equation). The fatigue limit (the stress below which failure does not occur) is determined. We report the S‑N curve, the fatigue limit, and the Basquin exponent.
• Strain‑life curve (ε‑N curve) determination (NTC 5811 – for the low‑cycle fatigue regime) – for high‑strain (low‑cycle) fatigue, we measure the strain amplitude (instead of the stress amplitude) and plot the strain‑life curve. The Coffin‑Manson parameters (the fatigue ductility coefficient and the fatigue ductility exponent) are determined. We report the ε‑N curve and the Coffin‑Manson parameters.
• Fatigue limit and endurance limit (NTC 5812 – for the infinite life design) – we perform a series of tests at decreasing stress amplitudes to identify the stress level at which the specimen survives a specified number of cycles (e.g., 10⁷ cycles) without failure. This stress level is the fatigue limit (or the endurance limit). We report the fatigue limit and the confidence interval.
• Statistical analysis of fatigue data (NTC 5813 – for the reliability assessment) – we perform a statistical analysis of the fatigue data (using the Weibull distribution or the log‑normal distribution) to estimate the fatigue life for a given reliability level (e.g., the B10 life – the life at which 10 % of the population fails). We report the Weibull parameters and the B10 life.
• Comparison with uniaxial fatigue data (NTC 5814 – for the multiaxial fatigue analysis) – we compare the biaxial fatigue life with the uniaxial fatigue life (from a standard uniaxial fatigue test) to determine the fatigue strength reduction factor due to the biaxial stress state. The comparison is expressed as a ratio (the biaxial fatigue factor). We report the biaxial fatigue factor and the interpretation.

Crack Initiation and Crack Propagation Monitoring – Evaluating the Damage Evolution

During the biaxial fatigue test, the evolution of damage (crack initiation and propagation) is monitored to understand the failure mechanism and to identify the critical locations. Our monitoring techniques include optical observation, potential drop measurement, and acoustic emission.

• Optical crack detection (NTC 5820 – for the surface crack observation) – we use a microscope (or a video camera) with a long‑distance objective to continuously observe the surface of the specimen during the test. The time to the first visible crack and the crack growth rate are recorded. We report the time to crack initiation, the crack length, and the crack growth rate.
• Potential drop method (NTC 5821 – for the continuous crack monitoring) – we pass a constant current through the specimen and measure the voltage drop across the gauge section. An increase in the voltage drop indicates the growth of a crack (which reduces the cross‑sectional area). The crack length is estimated from the voltage drop. We report the crack length vs. time curve and the crack growth rate.
• Acoustic emission monitoring (NTC 5822 – for the detection of the crack initiation) – we attach acoustic emission (AE) sensors to the specimen to detect the high‑frequency signals generated by the crack initiation and the crack propagation. The AE signals provide a real‑time indication of the damage. We report the AE activity and the time to crack initiation.
• Compliance method (NTC 5823 – for the stiffness‑based crack monitoring) – we measure the load‑displacement curve at regular intervals during the test. A decrease in the stiffness (the slope of the load‑displacement curve) indicates the growth of a crack. We report the stiffness degradation and the estimated crack length.
• Post‑test fractography (SEM – ASTM E1508 / NTC 5824 – for the failure mode analysis) – after the test, we examine the fracture surface using scanning electron microscopy (SEM) to identify the crack initiation site, the crack propagation path, and the failure mechanism (e.g., transgranular, intergranular, or mixed). We report the SEM images and the fractographic analysis.

Influence of Biaxial Stress Ratio and Phase Angle – Multiaxial Fatigue Criteria

The fatigue life under biaxial loading is strongly influenced by the stress ratio (the ratio of the two principal stresses) and the phase angle. Our tests evaluate the effect of these parameters, and we use the results to validate multiaxial fatigue criteria (such as the von Mises criterion, the Tresca criterion, and the Findley criterion).

• Biaxial stress ratio variation (NTC 5830 – for the effect of the stress distribution) – we perform the biaxial fatigue test at different stress ratios (e.g., σ_x / σ_y = 0, 0.5, 1, 2, ∞). The fatigue life is plotted against the stress ratio. We report the fatigue life at each stress ratio and the most damaging stress ratio.
• Phase angle variation (NTC 5831 – for the effect of the loading path) – we perform the biaxial fatigue test at different phase angles (e.g., 0°, 30°, 45°, 60°, 90°). The fatigue life is plotted against the phase angle. We report the fatigue life at each phase angle and the most damaging phase angle.
• Validation of the multiaxial fatigue criteria (NTC 5832 – for the design verification) – we compare the measured fatigue life with the life predicted by different multiaxial fatigue criteria (e.g., the von Mises equivalent stress, the Findley parameter, or the Fatemi‑Socie parameter). The criterion that best predicts the fatigue life is identified. We report the comparison and the recommendation for the design.
• Biaxial fatigue strength reduction factor (NTC 5833 – for the design code) – we calculate the biaxial fatigue strength reduction factor (the ratio of the uniaxial fatigue limit to the biaxial fatigue limit) and we express it as a function of the stress ratio and the phase angle. We report the reduction factor and the design curve.
• Numerical simulation correlation (NTC 5834 – for the finite element validation) – we use the experimental data (the S‑N curve, the crack initiation time, and the crack growth rate) to validate the finite element (FE) models of the component. The validated FE model is used to predict the fatigue life under different service conditions. We report the correlation and the FE validation.

Environmental and Temperature Effects – Evaluating the Durability under Service Conditions

The fatigue behavior of materials under biaxial loading can be significantly affected by the temperature, the humidity, and the presence of corrosive media. Our environmental tests simulate these conditions, providing a realistic assessment of the fatigue performance in the diverse Croatian climate (coastal, continental, and mountainous).

• High‑temperature biaxial fatigue test (NTC 5840 – for the power generation and aerospace applications) – we perform the biaxial fatigue test at elevated temperatures (e.g., 200 °C, 400 °C, 600 °C) using a heated test chamber (or an induction heating system). The fatigue life and the failure mode at the elevated temperature are reported. We report the fatigue life at each temperature and the temperature derating factor.
• Low‑temperature biaxial fatigue test (NTC 5841 – for the cold‑climate applications) – we perform the biaxial fatigue test at low temperatures (e.g., -20 °C, -40 °C) using a cryogenic chamber. The effect of the low temperature on the fatigue life and the ductility is evaluated. We report the fatigue life at the low temperature and the ductile‑to‑brittle transition (if applicable).
• Corrosive environment biaxial fatigue test (NTC 5842 – for the corrosion‑fatigue evaluation) – we perform the biaxial fatigue test in a corrosive environment (e.g., 3.5 % NaCl solution, salt spray, or acidic solution) by immersing the specimen in the corrosive medium during the test (or by applying a salt spray). The fatigue life in the corrosive environment is compared with the life in the inert environment. We report the corrosion‑fatigue life and the reduction factor.
• Humidity effect on biaxial fatigue (NTC 5843 – for the moisture‑sensitive materials) – we perform the biaxial fatigue test in a high‑humidity chamber (e.g., 40 °C, 95 % RH) to evaluate the effect of moisture on the fatigue performance (especially for polymers and composites). We report the fatigue life under the humid condition.
• Combined thermal‑mechanical fatigue (NTC 5844 – for the thermomechanical fatigue) – we subject the specimen to a combined cyclic temperature and cyclic mechanical load (with the temperature and the mechanical load cycling in phase or out of phase). The fatigue life under the combined loading is evaluated. We report the thermomechanical fatigue life and the failure mode.

Complementary Tests – Material Properties and Microstructure for Fatigue Correlation

To fully understand the fatigue behavior and to correlate it with the material's properties and microstructure, we perform complementary tests, including tensile testing, hardness testing, and microstructural examination.

• Tensile testing (ASTM E8 / ISO 6892 / NTC 5850 – for the yield and tensile strength) – we perform a tensile test on the material to determine the yield strength (MPa), the ultimate tensile strength (MPa), and the elongation (%). The tensile properties are correlated with the fatigue strength. We report the tensile properties and the correlation.
• Hardness testing (ASTM E18 / NTC 5851 – for the material strength) – we measure the hardness (Rockwell, Brinell, or Vickers) of the material to verify the heat treatment and the strength. The hardness is correlated with the fatigue resistance. We report the hardness and the correlation.
• Metallographic examination (ASTM E3 / NTC 5852 – for the grain size and the phase distribution) – we examine the microstructure (the grain size, the phase distribution, and the inclusion content) of the material using optical microscopy and SEM. The microstructure is correlated with the fatigue life and the crack initiation behavior. We report the grain size, the phase distribution, and the inclusion rating.
• Surface roughness measurement (ASTM D7127 / NTC 5853 – for the effect of the surface finish) – we measure the surface roughness (Ra, Rz) of the test specimen (before and after the fatigue test) using a profilometer. The surface roughness is correlated with the fatigue strength (a rougher surface reduces the fatigue life). We report the roughness values and the correlation.
• Residual stress measurement (XRD – NTC 5854 – for the effect of the residual stresses) – we measure the residual stresses in the specimen (using X‑ray diffraction) before the fatigue test. The residual stresses can affect the fatigue life (compressive residual stresses improve the life, while tensile residual stresses reduce it). We report the residual stress values and the effect on the fatigue life.

Test Report and Recognition in the Croatian Aerospace, Energy, and Industrial Sector

All procedures described are within the scope of our ISO/IEC 17025 accreditation, with equipment calibrated periodically (biaxial test machines, load cells, extensometers, and data acquisition systems) and traceability to international standards (NIST, PTB). Our test reports are issued in English (with a Croatian summary available on request) and include:

• Full identification of the test sample (material, thickness, orientation, and manufacturing process).
• Detailed description of the test methods applied (ASTM/ISO/HRN EN/NTC standards, stress ratio, phase angle, frequency, and temperature).
• Numerical results: fatigue life (cycles), S‑N curve parameters, fatigue limit (MPa), crack initiation time (cycles), crack growth rate (mm/cycle), and biaxial fatigue factor.
• Graphical data: S‑N curves, strain‑life curves, crack length vs. time curves, and load‑displacement curves.
• Comparative tables against the values specified by the client or against the limits of the relevant standards (ASTM E2207, ISO 1099, HRN EN ISO 1099, and the requirements of the HZN, Ministarstvo gospodarstva, and Državni inspektorat).
• SEM images of the fracture surfaces and the crack initiation sites.
• Recommendations for material selection, design optimization, and fatigue life improvement (e.g., shot peening, surface polishing, or the use of a stronger alloy).
• Expanded uncertainty (k=2) for all key measurements, calculated according to the ISO/IEC 98‑3 Guide.

These reports are fully accepted by the Hrvatski zavod za norme (HZN) for the verification of product conformity, by the Ministarstvo gospodarstva i održivog razvoja for industrial and energy compliance, by the Državni inspektorat for market surveillance, and by the Carinska uprava (Croatian Customs) for tariff classification and quality verification in the import of advanced materials and structural components. Additionally, we offer consulting services for the design of fatigue‑resistant structures, the selection of materials with high biaxial fatigue resistance, and the implementation of fatigue monitoring and maintenance programs, contributing to the safety, reliability, and longevity of critical infrastructure and industrial products in the diverse and growing Croatian market, from the aerospace and automotive sectors to the energy and manufacturing industries.