Interview Questions for Fracture Detection and Analysis

Brittle and ductile fracture represent two contrasting ways materials fail under stress. Think of it like breaking a glass versus bending a paperclip. A brittle fracture occurs suddenly with little to no plastic deformation. The material fails catastrophically without warning, often along specific crystallographic planes. Imagine shattering a ceramic mug – it breaks cleanly with sharp edges. Conversely, a ductile fracture involves significant plastic deformation before failure. This means the material stretches and deforms considerably before finally breaking. The paperclip, for example, stretches and bends extensively before snapping. The fracture surface will often be more irregular and fibrous.

The key difference lies in the material’s ability to absorb energy before failure. Brittle materials have low energy absorption capacity, while ductile materials absorb significantly more energy before fracture.

Fracture surfaces provide valuable clues about the cause and mechanism of failure. Several distinct types exist:

• Cleavage Fracture: This is a brittle fracture occurring along specific crystallographic planes of low atomic density within the material, resulting in a flat, shiny, and often faceted surface. Imagine a perfectly split piece of rock along its natural planes.
• Intergranular Fracture: This type of fracture occurs along the grain boundaries of a polycrystalline material. Grain boundaries are inherently weaker than the grains themselves. The resulting fracture surface is typically rough and irregular, reflecting the path taken along the weaker interfaces between grains. This is often seen in materials that have undergone corrosion or other grain boundary weakening processes.
• Transgranular Fracture: This occurs when the fracture path traverses through the grains, rather than along the grain boundaries. It’s frequently observed in ductile materials and can exhibit a variety of appearances depending on the failure mechanism (e.g., dimpled rupture in ductile fracture).
• Fatigue Fracture: Characterized by distinct regions indicating crack initiation, propagation, and final fracture. The surface often displays a characteristic beach mark pattern, resembling concentric circles, indicating incremental crack growth.

Examining fracture surfaces under a microscope can reveal crucial information about the material’s microstructure, loading conditions, and the failure mechanism.

Fracture detection methods range from simple visual inspection to sophisticated non-destructive testing (NDT) techniques. Common methods include:

• Visual Inspection: The simplest method, involving careful examination of the component for any visible cracks, flaws, or unusual surface features. This is often the first step in any fracture analysis.
• Liquid Penetrant Testing (LPT): A dye is applied to the surface, penetrating any cracks or flaws. A developer then draws the dye out, revealing the defects as visible indications. Useful for detecting surface cracks in many materials.
• Magnetic Particle Testing (MPT): Used for ferromagnetic materials, magnetic particles are applied to the surface, and a magnetic field is induced. The particles accumulate at the location of defects, making them visible.
• Ultrasonic Testing (UT): Uses high-frequency sound waves to detect internal flaws. Reflections of the sound waves indicate the presence and location of cracks or other defects (explained further in the next question).
• Radiographic Testing (RT): Uses X-rays or gamma rays to create an image of the internal structure of a component, revealing the presence of internal cracks or other defects (also explained further in the next question).

Ultrasonic Testing (UT) uses high-frequency sound waves (typically above the range of human hearing) that are transmitted into the material. These waves propagate through the material and are reflected by discontinuities like cracks. By measuring the time it takes for the reflected waves to return, the location and size of the defect can be determined. Think of it like sonar, but for internal flaws in materials. A skilled technician interprets the resulting signals (A-scans, B-scans, C-scans) to identify and characterize defects.

Radiographic Testing (RT) utilizes X-rays or gamma rays to penetrate the material. The denser areas of the material absorb more radiation, while defects such as cracks allow more radiation to pass through. The resulting image (radiograph) reveals the internal structure and any flaws present. Imagine taking a shadow picture of the inside of the component; areas with less density will appear darker on the radiograph, thus highlighting the defect.

Fracture toughness is a crucial material property that dictates a material’s resistance to crack propagation. It’s essentially a measure of how much stress a material can withstand before a crack starts to grow. When selecting materials for critical applications, such as aircraft components or pressure vessels, fracture toughness is a paramount consideration. Materials with high fracture toughness are preferred for applications where crack initiation and propagation pose a risk. For instance, high-strength steel alloys with high fracture toughness are often used in aircraft structures to prevent catastrophic failure from small cracks.

A low fracture toughness value indicates that a crack will grow easily under relatively low stress levels, making the material brittle and susceptible to failure. Conversely, a high fracture toughness value signifies greater resistance to crack growth and, consequently, increased structural reliability.

The stress intensity factor (K) is a critical parameter in fracture mechanics that quantifies the stress field at the tip of a crack. It’s a measure of how intense the stress is concentrated at the crack tip. A higher K value indicates a more intense stress concentration, increasing the likelihood of crack propagation. The stress intensity factor is dependent on the crack geometry (size and shape), applied load, and material properties. Different geometries and loading conditions have different formulas for calculating K. For instance, a common formula for a crack under mode I (opening mode) loading is:

where:

• K is the stress intensity factor
• Y is a dimensionless geometric factor depending on the crack and specimen geometry
• σ is the applied stress
• a is the crack length

In fracture mechanics, the stress intensity factor is used in conjunction with the material’s fracture toughness (K_IC) to predict crack propagation. If K exceeds K_IC, the crack will propagate.

Fatigue crack growth refers to the gradual propagation of cracks under cyclic loading conditions (repeated application and removal of stress). Even if the maximum stress during each cycle is below the material’s yield strength, repeated stress cycles can lead to crack initiation and progressive growth, eventually resulting in failure. Think of a paperclip repeatedly bent back and forth – it will eventually break, even if you never apply enough force to break it directly in a single bending action.

The rate of fatigue crack growth depends on several factors, including the applied stress range, the material’s properties (fatigue strength), the crack geometry, and the environment. Understanding fatigue crack growth is crucial in designing components subjected to cyclic loading, such as aircraft wings, turbine blades, or bridge structures. Fatigue crack growth is typically modeled using empirical relationships, such as Paris’ law, which relates crack growth rate to the stress intensity factor range.

The J-integral is a path-independent line integral used in fracture mechanics to characterize the energy release rate during crack propagation. Imagine a crack tip as a point of intense stress concentration. The J-integral essentially quantifies the energy needed to extend that crack by a unit length. It’s a crucial parameter because it allows us to predict when a crack will start to grow and at what rate, regardless of the specific geometry of the component or the loading conditions. A higher J-integral value indicates a greater driving force for crack growth, meaning the material is closer to failure.

Significance: The J-integral is particularly useful for analyzing crack growth in ductile materials under nonlinear elastic-plastic conditions, where simpler linear elastic fracture mechanics (LEFM) approaches are inadequate. It forms the basis for various fracture toughness testing standards and is widely used in engineering design to ensure structural integrity.

Example: Consider a pressure vessel with a pre-existing crack. Using finite element analysis (FEA) and calculating the J-integral, engineers can determine if the vessel is safe to operate at a given pressure, or if the crack will propagate, leading to catastrophic failure. The J-integral value provides a quantitative measure of the remaining safety margin.

Crack propagation is the process by which a crack extends in a material, eventually leading to failure. It’s the crucial step that transforms a small imperfection into a catastrophic event. The way a crack grows is heavily influenced by the material properties, loading conditions, and the environment. Crack propagation isn’t just a simple lengthening; it can involve complex branching, curving, or even arrest (stopping). This behavior dictates the overall failure mode, whether it is brittle (sudden and catastrophic), ductile (with significant plastic deformation before failure), or a combination of both.

Role in Material Failure: A crack acts as a stress concentrator, meaning that the stresses at the crack tip are significantly higher than the average stress in the material. As the crack grows, the stress concentration intensifies, leading to an accelerating growth rate until the material ultimately fails. The initiation and propagation of cracks are fundamental aspects of material failure analysis.

Example: Consider a fatigue crack in an aircraft wing. Each cycle of loading causes the crack to grow incrementally. Eventually, the crack reaches a critical size where the stress intensity at the tip is sufficient to cause rapid propagation, leading to a potential catastrophic failure of the wing.

Several models describe crack growth, the most common being Paris Law. These models relate the rate of crack growth (da/dN, where ‘a’ is crack length and ‘N’ is the number of load cycles) to the stress intensity factor (K) at the crack tip. The stress intensity factor essentially represents the magnitude of stress at the crack tip. Different models account for varying factors like material properties and loading conditions.

• Paris Law: This empirical model is the most widely used and states that da/dN = CΔKm, where C and m are material constants determined experimentally. ΔK represents the range of stress intensity factor during cyclic loading.
• Other Models: More advanced models, such as Forman’s equation and Walker’s equation, consider additional factors like the threshold stress intensity (K_th) below which crack growth is negligible and the critical stress intensity (K_c) that causes rapid crack propagation.

Practical Application: These models are critical for predicting the fatigue life of components subjected to cyclic loading. By characterizing the material constants (C and m) through fatigue testing, we can estimate how long a component with an initial crack will last before failure. This allows engineers to implement appropriate safety factors and maintenance schedules.

Fractography is the study of fracture surfaces to understand the cause and mechanism of failure. Interpreting fractographic images involves careful observation of the fracture surface features, such as the fracture origin, crack path, and the characteristic markings left behind. These markings provide valuable clues about the loading conditions, the rate of crack propagation, and the material’s fracture behavior.

• Features to Look For: Brittle fracture surfaces often exhibit radial markings (hackle marks) emanating from the origin, while ductile fractures display dimples formed by plastic deformation. Fatigue fractures are characterized by distinct beach marks (also called striations), representing periods of crack growth during cyclic loading. Other features like cleavage facets (planar facets indicative of brittle cleavage fracture) or tear ridges (indicating shear fracture) are also significant indicators.
• Magnification: Often, magnification using optical or scanning electron microscopy is crucial for detailed analysis.

Example: A fractographic image showing beach marks indicates that the failure was due to fatigue, likely caused by repeated stress cycles. The spacing and size of these marks can even provide information about the load amplitude and the rate of crack propagation.

Failure analysis is a systematic investigation to determine the cause of a component or structure’s failure. It’s a crucial process in many engineering disciplines to prevent similar failures in the future. The analysis typically includes several steps:

1. Information Gathering: Collect information about the failure – such as operating conditions, service history, and the environment.
2. Visual Inspection: Examine the failed component for macroscopic evidence of damage, including cracks, deformations, and fracture surfaces.
3. Fractographic Analysis: Conduct detailed examination of fracture surfaces using optical and electron microscopy to determine the failure mechanism.
4. Material Characterization: Perform tests such as tensile testing, hardness testing, and chemical analysis to understand the material properties.
5. Stress Analysis: Use analytical or numerical methods (such as FEA) to analyze stress distribution in the component and assess if stress levels exceeded the material’s capacity.
6. Report Writing: Document the findings and conclusions, recommending improvements to design, materials, or operation to prevent future failures.

Example: Imagine a bridge collapse. A failure analysis would involve examining the failed structural members, analyzing stress levels under various loading conditions, determining material properties, and evaluating the design’s adequacy to prevent similar catastrophic failures in other bridge structures.

Many factors influence fracture behavior, significantly impacting a material’s resistance to crack initiation and propagation. These factors can be broadly categorized into material properties, loading conditions, and environmental factors.

• Material Properties: These include the material’s strength, toughness (resistance to crack propagation), ductility (ability to deform plastically before failure), grain size, and microstructure. The presence of defects, inclusions, or residual stresses within the material also plays a vital role.
• Loading Conditions: The type of loading (static, dynamic, cyclic), the magnitude and rate of loading, the stress state (tensile, compressive, shear), and the presence of stress concentrations all influence fracture behavior.
• Environmental Factors: Corrosion, temperature, humidity, and radiation can significantly impact a material’s strength and fracture resistance. The presence of aggressive chemicals can accelerate crack initiation and propagation.

Example: A high-strength steel component might exhibit brittle fracture at low temperatures, while the same component might show ductile behavior at room temperature. This difference is primarily due to the effect of temperature on material properties like ductility and toughness.

The distinction between static and dynamic fracture lies primarily in the loading rate. Static fracture occurs under slowly applied loads, allowing for significant plastic deformation in ductile materials before fracture. Think of a simple tensile test. In contrast, dynamic fracture involves rapidly applied loads, such as impacts or explosions, often resulting in brittle fracture. The higher loading rates in dynamic fracture leave less time for plastic deformation, leading to crack propagation at much higher velocities.

Key Differences:

• Loading Rate: Static fracture involves slow loading rates, while dynamic fracture occurs under rapid loading.
• Ductility: Ductile materials often exhibit significant plastic deformation before failure in static fracture but can fracture in a brittle manner under dynamic loading.
• Crack Propagation Velocity: Crack propagation velocity is generally much higher in dynamic fracture compared to static fracture.
• Failure Modes: Failure modes can vary significantly, with ductile fracture more common in static loading and brittle fracture more prevalent in dynamic loading.

Example: A slowly applied tensile load on a ductile metal specimen will lead to a neck formation and then ductile fracture, whereas a high-velocity impact on the same material might result in brittle fracture, potentially shattering the specimen.

The Griffith criterion is a fundamental concept in fracture mechanics that determines the conditions under which a crack will propagate in a brittle material. It states that a crack will grow when the energy released by the crack propagation is greater than the energy required to create new crack surfaces. Think of it like this: if the energy gained by relieving stress around the crack is more than the energy it takes to break the bonds at the crack tip, the crack will advance.

Mathematically, this is expressed as:

where:

• γ is the surface energy of the material (energy required to create new surfaces).
• σ is the applied stress.
• a is the crack length (half the crack length for a through crack).
• E is the Young’s modulus (a measure of the material’s stiffness).

The criterion highlights the crucial role of crack length. Even under low stress, a sufficiently large crack can propagate, emphasizing the importance of crack detection and prevention.

Environmental factors significantly influence fracture behavior, often accelerating crack growth and reducing the material’s fracture toughness. For instance, corrosive environments can initiate and propagate stress corrosion cracking, where the combined action of stress and chemical attack leads to crack formation and propagation. Imagine a metal bridge constantly exposed to salt water; the salt accelerates corrosion, weakening the bridge’s structure and potentially causing catastrophic fracture.

Other environmental effects include:

• Hydrogen Embrittlement: Hydrogen atoms can diffuse into the material, reducing its ductility and making it more susceptible to cracking.
• Temperature: High temperatures can reduce material strength and accelerate crack growth, while low temperatures can increase brittleness.
• Moisture: Moisture can contribute to corrosion and reduce the material’s resistance to fatigue.

Understanding these environmental influences is critical in material selection and design to ensure structural integrity and safety.

Preventing fracture involves a multi-pronged approach focusing on material selection, design considerations, and operational practices. The most effective strategy is a combination of these elements.

Here’s a breakdown of preventative measures:

• Material Selection: Choosing materials with high fracture toughness, good fatigue resistance, and corrosion resistance appropriate for the operating environment is paramount. For instance, using stainless steel instead of mild steel in a corrosive environment.
• Design Optimization: Reducing stress concentrations, such as using fillets instead of sharp corners, incorporating stress relieving features, and optimizing geometry to avoid stress-raising flaws are essential. Finite Element Analysis (FEA) plays a crucial role in this step.
• Manufacturing Processes: Careful control of manufacturing processes to minimize defects such as inclusions, porosity, and cracks is critical. Regular quality control and non-destructive testing help catch these imperfections early.
• Regular Inspection and Maintenance: Periodic inspections, often including non-destructive testing (NDT) techniques like ultrasonic testing or radiography, to detect cracks and other flaws before they propagate is crucial for ongoing safety.
• Operational Procedures: Ensuring safe operational practices that avoid overstressing components and providing proper maintenance procedures also contributes significantly.

The optimal approach depends heavily on the specific application and operating conditions. A thorough risk assessment helps tailor these preventative measures effectively.

My experience with Finite Element Analysis (FEA) in fracture mechanics is extensive. I have utilized FEA software such as ANSYS and ABAQUS to model crack propagation, determine stress intensity factors (K), and predict crack growth under various loading conditions. I’ve worked on projects involving everything from the simulation of crack growth in pressure vessels to the analysis of fatigue cracks in aircraft components.

A recent project involved using FEA to model and predict the lifespan of a turbine blade under cyclic loading. By simulating the crack initiation and propagation under different operating conditions, we were able to optimize the blade design, enhancing its fatigue life and preventing catastrophic failure. The results from the FEA were validated with experimental data, demonstrating the accuracy of the model. We also used this model to explore the effects of different surface treatments and material properties on crack growth.

Several standardized methods are used to measure fracture toughness. The choice of method depends on the material type and the type of fracture expected.

Key methods include:

• Plane Strain Fracture Toughness (K_IC): This test, often performed on specimens of specific dimensions to ensure plane strain conditions, determines the critical stress intensity factor required for crack propagation under plane strain conditions. It’s applicable to brittle and ductile materials and widely used for metallic materials.
• Compact Tension (CT) Specimen: This is a popular geometry used in the determination of K_IC due to its ease of testing and analysis. The specimen geometry promotes a consistent stress field at the crack tip.
• Three-Point Bend (3PB) Specimen: Another commonly used specimen geometry which uses a simple loading configuration to determine fracture toughness. It is appropriate for a wider range of materials and test conditions.
• J-Integral Approach (J_IC): This approach is particularly useful for ductile materials undergoing large-scale yielding at crack tips. It is a more energy-based approach that accounts for plastic deformation.

The selection of appropriate test method and the proper interpretation of the test results are crucial for accurate material characterization and safe design.

Determining the critical crack size involves understanding the relationship between the applied stress, crack length, and the material’s fracture toughness. The critical crack size (a_c) is the crack size at which unstable crack propagation occurs.

For brittle materials, the critical crack size can be estimated using the Griffith criterion or its more advanced forms considering stress intensity factors. The formula is:

where:

• a_c is the critical crack size.
• K_IC is the plane-strain fracture toughness of the material.
• σ is the applied stress.

For ductile materials, the analysis is more complex, often involving numerical methods such as FEA to estimate J-integral and account for plastic deformation. In practice, a safety factor is always added to ensure a wide margin of safety.

Numerous fracture prevention techniques are used in engineering applications to enhance structural integrity and prevent catastrophic failures. These techniques can be broadly categorized into design, material selection, and manufacturing strategies.

Common techniques include:

• Crack Arresters: These are design features that limit crack propagation. Common examples include adding blunt notches or other geometric features to impede crack growth.
• Redundancy: Designing structures with multiple load paths ensures that failure in one component doesn’t lead to a complete system collapse.
• Stress Relieving Techniques: Heat treatments can reduce residual stresses in materials after manufacturing, making them less prone to cracking.
• Surface Treatments: Shot peening or other surface treatments introduce compressive residual stresses, enhancing fatigue resistance and reducing crack initiation.
• Fatigue Strengthening: Selecting materials with high fatigue strength and using design techniques to minimize cyclic loading are essential to prevent fatigue crack growth.
• Non-Destructive Testing (NDT): Regular inspection utilizing techniques like ultrasonic testing, radiography, or liquid penetrant testing can detect flaws before they grow to critical sizes.
• Crack Growth Monitoring: Regular monitoring of crack growth through periodic inspections can provide advance warnings before failure.

The selection of appropriate techniques depends on the nature of the loading, the material, and the specific design. A comprehensive approach often combines several methods for optimal fracture prevention.

Discovering a potential fracture in a critical component demands a methodical approach prioritizing safety and thorough investigation. My first step would be to immediately isolate the component to prevent further damage or risk. Then, I’d initiate a detailed visual inspection, documenting the location, size, and appearance of the suspected fracture using high-resolution photography and potentially microscopic imaging. This initial visual assessment helps determine the severity and potential propagation path of the crack. Next, I would employ non-destructive testing (NDT) techniques such as dye penetrant testing, ultrasonic testing, or radiography to confirm the presence, extent, and nature of the fracture. The choice of NDT method depends on the material, component geometry, and access limitations. Finally, based on the NDT results and the criticality of the component, I would determine whether repair, replacement, or further analysis (e.g., fracture mechanics analysis) is necessary. This decision would involve considering safety factors, operating conditions, and potential consequences of failure.

For example, imagine finding a crack in a turbine blade of a jet engine. The immediate isolation would prevent catastrophic failure during flight. Subsequent NDT and fracture analysis would determine the crack’s growth rate and remaining useful life. This information would be crucial in making informed decisions about repair or replacement, ensuring flight safety.

My expertise spans a range of software and tools used in fracture analysis. I’m proficient in finite element analysis (FEA) software such as ANSYS and ABAQUS, which I utilize to model crack propagation, stress intensity factor calculations, and fatigue life predictions. For image processing and analysis of NDT results, I utilize software like ImageJ and specialized packages within MATLAB. I am also comfortable working with dedicated fracture mechanics software packages that provide specialized tools for crack growth simulation and analysis. For data management and reporting, I use platforms like Python with relevant libraries such as SciPy and Pandas. Finally, I’m skilled in using various data acquisition systems interfacing with NDT equipment to acquire and analyze data.

My experience encompasses a wide spectrum of NDT techniques, each with its strengths and limitations. I’ve extensively used visual inspection (VI), which serves as a preliminary assessment for identifying surface defects. Dye penetrant testing (PT) is invaluable for detecting surface-breaking cracks in non-porous materials. Ultrasonic testing (UT) allows for the detection of both surface and subsurface flaws through the use of high-frequency sound waves. Radiographic testing (RT), employing X-rays or gamma rays, provides a comprehensive view of internal defects, particularly in thicker sections. Acoustic emission (AE) is particularly useful for monitoring crack growth in real-time. I’ve also worked with magnetic particle testing (MT) to detect surface and near-surface flaws in ferromagnetic materials. The choice of the appropriate NDT method is guided by the type of material, component geometry, expected flaw type, and access considerations. For instance, UT is better suited for inspecting thick components whereas PT works well for surface cracks in intricate parts.

Ensuring accuracy and reliability in fracture analysis is paramount. This involves a multi-faceted approach. First, meticulous data acquisition is crucial, employing calibrated equipment and standardized procedures for all NDT methods. Data from multiple NDT techniques are often compared and validated against each other. Second, proper sample preparation is vital. This includes careful cleaning, surface preparation, and accurate dimensional measurements to minimize errors. Third, the chosen analytical methods must be appropriate for the material and type of fracture. For instance, the use of appropriate fracture mechanics models is necessary and requires understanding of the material’s constitutive behavior. Fourth, uncertainty analysis is incorporated to quantify the uncertainty associated with measurements and model predictions. Lastly, verification and validation are essential. This involves comparing analysis results with experimental data or historical data where possible. If discrepancies exist, a thorough investigation is undertaken to identify the source of error and refine the analysis.

Despite significant advancements, current fracture analysis techniques have limitations. One key limitation lies in accurately predicting crack initiation and propagation in complex geometries and under multiaxial loading conditions. Current models often simplify complex material behavior, neglecting factors like microstructural effects, residual stresses, and environmental influences. Another limitation is the difficulty in reliably characterizing the fracture properties of advanced materials, such as composites or functionally graded materials, which exhibit complex microstructures and mechanical behaviors. Additionally, the detection and characterization of very small or hidden cracks remain a challenge, especially in complex components. Finally, the cost and time associated with some advanced analysis techniques, such as three-dimensional finite element modeling, can be significant.

Material microstructure plays a crucial role in dictating fracture behavior. The grain size, grain orientation, presence of precipitates, inclusions, and defects all significantly influence a material’s strength, ductility, and fracture toughness. For example, fine-grained materials generally exhibit higher strength and yield strength but can be more brittle than coarse-grained materials. The presence of voids, inclusions, or other microstructural defects can act as stress concentrators, initiating cracks and reducing fracture toughness. Furthermore, grain boundary characteristics play a role; materials with weak grain boundaries are more susceptible to intergranular fracture. Understanding the microstructure is essential for accurately predicting fracture behavior; therefore, techniques like microscopic analysis (optical, SEM, TEM) are used to characterize microstructure and understand its influence on fracture.

Consider the difference between a ductile material like mild steel and a brittle material like glass. Mild steel’s microstructure allows for significant plastic deformation before fracture, absorbing energy and leading to higher toughness. Glass, on the other hand, has a less ordered structure and lacks significant plasticity, leading to brittle fracture.

To determine the fracture toughness of a material, I’d design an experiment based on established standards, such as ASTM E399 (for plane-strain fracture toughness, K_IC). The experiment typically involves preparing standardized specimens with pre-existing cracks (e.g., compact tension (CT) or three-point bend (3PB) specimens). These specimens are then subjected to controlled loading conditions until fracture occurs. The load at fracture and the crack length are measured precisely. Using these measurements and appropriate equations (derived from linear elastic fracture mechanics), the fracture toughness (K_IC or J_IC) can be calculated. Multiple specimens would be tested to ensure reproducibility and to account for inherent material variability. During testing, precise control of temperature and loading rate are crucial, as fracture toughness is sensitive to these factors. Careful examination of the fracture surfaces would also provide insights into the fracture mechanism. The choice of specimen type and testing technique would depend on the material’s properties and thickness. For example, thicker sections would require plane strain testing conditions, while thin specimens might necessitate plane stress analysis.