What are the three distinct modes of crack propagation in fracture mechanics?
Explanation
This question tests the basic terminology for classifying how a crack can propagate based on the relative displacement of its surfaces. Understanding these three modes is fundamental to applying fracture mechanics.
Other questions
What are the defining characteristics of a static load as applied to a mechanical member?
When analyzing a ductile material under a static load where elastic behavior is expected, what value is typically assigned to the geometric stress-concentration factor, Kt?
For which of the following brittle materials is it often acceptable to not apply the theoretical stress-concentration factor Kt in a static loading analysis?
According to the Maximum-Shear-Stress (MSS) theory for ductile materials, what is the predicted relationship between the shear yield strength (Ssy) and the tensile yield strength (Sy)?
The Distortion-Energy (DE) theory for ductile materials predicts that the shear yield strength (Ssy) is what fraction of the tensile yield strength (Sy)?
What is the primary material property distinction used in the chapter to separate failure theories into 'ductile' and 'brittle' categories?
For a general state of plane stress, the von Mises stress (σ') can be expressed in terms of the Cartesian stress components (σx, σy, τxy). What is this expression?
A hot-rolled steel with a yield strength Sy = 100 kpsi is under a plane stress state where σx = 70 kpsi and σy = 70 kpsi. Using the Distortion-Energy theory, what is the von Mises stress σ'?
For a plane stress state where the principal stresses are σA = 69.2 kpsi and σB = -29.2 kpsi, and the material yield strength is Sy = 100 kpsi, what is the factor of safety according to the Maximum-Shear-Stress (MSS) theory?
The Distortion-Energy (DE) theory was developed from the observation that yielding in ductile materials was not a simple tensile or compressive phenomenon, but was related to what physical action?
What is the primary advantage of the Ductile Coulomb-Mohr theory over the Maximum-Shear-Stress or Distortion-Energy theories?
A 25-mm-diameter shaft made of cast 195-T6 aluminum (Syt = 160 MPa, Syc = 170 MPa) is subjected to a pure static torque that produces a maximum shear stress of 75 MPa. Using the Ductile Coulomb-Mohr theory, what is the factor of safety?
According to the summary of failure theories for ductile materials and the experimental data presented in Figure 5-15, which theory is generally considered a better predictor of failure, passing closer to the central area of data points?
The force F required to initiate yielding in a component is regarded as what property of that component?
A cantilevered bar of AISI 1035 steel with Sy = 81 kpsi is subjected to loading that produces a tensile bending stress of σx = 142.6F and a torsional stress of τzx = 76.4F at the critical point. Using the Distortion-Energy theory, what is the force F that will initiate yielding?
What is the fundamental principle of the Maximum-Normal-Stress (MNS) theory for brittle materials?
For a brittle material under plane stress with σA ≥ 0 and σB ≤ 0, which design equation represents the Brittle-Coulomb-Mohr (BCM) theory?
A wrench made of ASTM grade 30 cast iron (Sut = 31 kpsi, Suc = 109 kpsi) is loaded such that the principal stresses at the critical point are σA = 175.8F and σB = -33.2F. Using the Brittle-Coulomb-Mohr failure model, what is the force F that will cause fracture?
According to the flowchart for selecting failure criteria (Figure 5-21), what is the first question you should ask to decide between ductile and brittle failure theories?
What is the primary reason that elastic stress-concentration factors (Kt) are considered inadequate for analyzing parts with very sharp cracks?
In Linear Elastic Fracture Mechanics (LEFM), what term is used for the material property that defines the critical value of the stress intensity factor at which a crack begins to propagate?
What is the basic formula for the mode I stress intensity factor (KI) for an infinite plate with a central crack of length 2a subjected to a remote tensile stress σ?
In the context of fracture mechanics, what does the stress intensity modification factor, β, account for?
A steel ship deck plate is operated below its ductile-to-brittle transition temperature, giving it a fracture toughness KIc of 28.3 MPa-sqrt(m). It has a 65-mm-long central transverse crack (2a = 65 mm). What tensile stress, σc, will cause catastrophic failure?
In Example 5-7, two titanium alloys are considered for a plate supporting a tensile force. Alloy 1 (weaker) has Sy = 910 MPa and KIc = 115 MPa-sqrt(m). Alloy 2 (stronger) has Sy = 1035 MPa and KIc = 55 MPa-sqrt(m). Why does the weaker alloy lead to a thinner and lighter design?
What is the primary reason the Soderberg failure criterion is considered ultra-conservative?
Which ductile failure theory is graphically represented by a hexagon in the σA, σB plane stress space?
What is the physical interpretation of the von Mises stress, σ'?
A ductile material is subjected to a stress state where the three principal stresses are equal: σ1 = σ2 = σ3 = 30 kpsi. What is the von Mises stress σ'?
When comparing the failure envelopes for the Distortion-Energy (DE) and Maximum-Shear-Stress (MSS) theories for a ductile material with equal tensile and compressive strengths, which statement is true?
For the Modified Mohr (MM) theory for brittle materials under plane stress, which quadrant of the stress-state plane does it primarily seek to improve upon compared to the Brittle-Coulomb-Mohr (BCM) theory?
The term 'damage-tolerant design' is a philosophy focused on what main idea?
A steel tube has an outside diameter of 42 mm. The material has an ultimate strength of 440 MPa. Using the formula ka = a * Sut^b and the parameters for a machined surface from Table 6-2 (a=3.04, b=-0.217), what is the estimated surface factor ka?
For the three-dimensional von Mises stress, what is the correct formula in terms of the principal stresses σ1, σ2, and σ3?
A material has a yield strength Sy = 100 kpsi and is in a plane stress state with σx = 0, σy = 40 kpsi, and τxy = 45 kpsi. What is the von Mises stress σ'?
What is the factor of safety guarding against yielding for a material with Sy = 100 kpsi under a stress state where the von Mises stress is calculated to be σ' = 59.0 kpsi?
In the comparison of failure theories for the biaxial fracture of gray cast iron shown in Figure 5-19, which theory provides the best fit for data in the fourth quadrant (tension-compression)?
The design flowchart in Figure 5-21 suggests a choice between Distortion-Energy (DE) and Maximum-Shear-Stress (MSS) for ductile materials with Syt ≈ Syc. What question does it pose to help make this choice?
In a static loading situation of a ductile material, what is the rationale for setting the stress concentration factor Kt to unity?
What is the primary difference in the failure criteria equations for the Brittle-Coulomb-Mohr theory versus the Ductile-Coulomb-Mohr theory?
For the plane stress condition, Case 1 of the Maximum-Shear-Stress theory occurs when σA ≥ σB ≥ 0. What is the resulting yield condition?
A factor of safety in the context of the graphical failure envelopes, such as in Figure 5-7, can be interpreted as the ratio of what two distances?
In the summary of ductile failure theories, why is the Distortion-Energy (DE) theory generally preferred over the Maximum-Shear-Stress (MSS) theory for analysis, even though MSS is simpler?
A torque wrench component made of AISI 1035 steel with Sy = 81 kpsi is analyzed using two different failure theories. The Distortion-Energy theory predicts a failure force of 416 lbf, while the Maximum-Shear-Stress theory predicts 388 lbf. Which theory is more conservative in this case?
What is the factor of safety, n, according to the Coulomb-Mohr theory if σ1 = 75 MPa, σ3 = -75 MPa, Syt = 160 MPa, and Syc = 170 MPa?
When using the selection flowchart in Figure 5-21 for a ductile material where the tensile yield strength is NOT approximately equal to the compressive yield strength, which failure theory is recommended?
What is the primary reason that the Maximum-Normal-Stress theory is not recommended for use, despite its simplicity?
For a cantilevered tube made of 2014 aluminum alloy with a yield strength of 276 MPa, the critical stress element is subjected to a normal stress σx = 9/A + 105do/I and a torsional stress τzx = 36do/J. What is the formula for the von Mises stress, σ', based on these components?
The factor of safety can be defined as the ratio of strength to stress. For fracture mechanics, what is the analogous expression for the factor of safety, n?