Mechanical Properties: 2 MSC101: Eyres

Chapter Learning Objectives Using energy arguments, explain why flaws in a material may lead to premature fracture Define fracture toughness and calculate it and the critical flaw size for a material Define the fracture mechanics relationship between the material properties, the stress applied, and the flaw size Identify the morphology of failure surfaces that indicate whether ductile or brittle fracture occurred Describe the process of fatigue Explain why fatigue occurs and quantify fatigue behavior Describe the process of creep © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. 7-1 Fracture Mechanics Fracture mechanics is the discipline concerned with the behavior of materials containing cracks or other small flaws The term “flaws” refers to such features as pores, inclusions, or microcracks. It does not refer to atomic level defects such as vacancies or dislocations Fracture toughness measures the ability of a material containing a flaw to withstand applied load Fracture toughness may be tested by applying a tensile test to a specimen prepared with a flaw of known size and geometry The stress applied to the material is intensified at the flaw. The stress intensity factor is given by Equation 7-1, which contains geometric factor f, applied stress σ, and crack size a By testing, we determine the value of K that causes the flaw to grow and cause failure. This value is defined as the fracture toughness Kc © 2014 Cengage Learning Engineering. All Rights Reserved.

Fracture Toughness and Resisting Factors Fracture toughness depends on the thickness of the sample: as thickness increases, Kc decreases to a constant value This value is called the plane strain fracture toughness Kic The ability of a material to resist the growth of a crack depends on a large number of factors, some of which are: Ductility (Kc) or Brittleness (Kc) Thicker (Kc) or thinner (Kc) Faster (Kc) or slower (Kc) rate of application of the load Increasing (Kc) or decreasing (Kc) temperature © 2014 Cengage Learning Engineering. All Rights Reserved.

The Importance of Fracture Mechanics Fracture mechanics allows us to design and select materials while taking into account the inevitable presence of flaws There are three variables to consider: the size of the flaw, a the property of the material, Kc or Kic the maximum stress the material must withstand, σ If we know (1) and (3), we can select a material with the appropriate fracture toughness to prevent the flaw from growing If we know (1) and (2), we can calculate the maximum stress a component can withstand and design it to ensure it does not exceed that stress Finally, if we know (2) and (3), we can calculate the maximum size of a flaw that can be tolerated © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Brittle Fracture Any crack limits the ability of a ceramic to withstand a tensile stress, because cracks concentrate and magnify the applied stress The actual stress at the crack tip can be found through Equation 7-3 If the actual stress exceeds the yield strength, the crack propagates Alternatively, by energy methods, we derive Equation 7-4 for the stress needed to propagate the crack This is just Eq 7-1 again. © 2014 Cengage Learning Engineering. All Rights Reserved.

Microstructural Features of Fracture in Metallic Materials Two aspects of ductile fracture give it distinctive features: that it occurs in a trangranular (through the grains) manner, with microvoids forming at grain boundaries that slip also contributes, with the highest resolved shear stress at a 45° angle to the applied stress Thus a ductile fracture will typically display: necking with a flat face where microvoids nucleated and coalesced a small shear lip where the fracture surface is 45° to the applied stress © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Brittle Fracture A brittle fracture can be identified by features on the failed surface Normally, the surface is flat and perpendicular to the applied stress However, if failure occurred by cleavage, each fractured grain is oriented differently, giving the surface a “rock candy” look Another common fracture feature is the Chevron pattern, produced by separate crack fronts propagating at different levels in the material © 2014 Cengage Learning Engineering. All Rights Reserved.

Microstructural Features of Fracture in Ceramics and Glasses In ceramics, the ionic or covalent bonds permit little or no slip, and so failure is a result of brittle fracture The fracture surface is typically smooth, and frequently no characteristic feature points to the origin of the fracture Glasses also fracture in a brittle manner. Frequently a conchoidal fracture surface is observed. This surface contains a smooth mirror zone near the origin of the fracture and tear lines comprising the remainder of the surface © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Fatigue Fatigue is the lowering of strength or failure of a material due to repetitive stress that may be above or below the yield strength Fatigue failures typically occur in three stages: A tiny crack nucleates, often well after loading begins The crack gradually propagates as the load continues to cycle A sudden fracture occurs when the remaining cross- section is too small to support the load Fatigue failures are often easy to identify by the characteristic features they leave on the fracture surface (see Figure 7-15) © 2014 Cengage Learning Engineering. All Rights Reserved.

© 2014 Cengage Learning Engineering. All Rights Reserved. Fatigue Test One method for testing a material’s resistance to fatigue is the rotating cantilever beam test, pictured to the right In the test, the stress at any one point on the specimen goes through a complete sinusoidal cycle from maximum tensile to maximum compressive stress The results of such a test are usually presented in a S-N curve (also known as the Wöhler curve), as seen to the right © 2014 Cengage Learning Engineering. All Rights Reserved.

Results of the Fatigue Test The fatigue test can tell us how long a part may survive or the maximum allowable loads that can be applied without causing failure The endurance limit is the stress below which there is a 50% probability that failure by fatigue will never occur. It is the preferred design criterion, though it should be treated with caution since research has shown that it does not exist for many materials Fatigue life tells us how long a component will last at a particular stress Fatigue strength is the maximum stress for which fatigue will not occur within a particular number of cycles © 2014 Cengage Learning Engineering. All Rights Reserved.

Creep, Stress Rupture, and Stress Corrosion Creep is time-dependent, permanent deformation under constant load or constant stress and at high temperatures A material is considered failed by creep even if it has not fractured. When a material does creep and then ultimately breaks, the fracture is called a stress rupture Stress corrosion is a phenomenon in which materials react with corrosive chemicals in the environment. This leads to the formation of cracks and the lowering of strength Tempering glass produces an overall compressive stress on the surface of the glass and prevents cracks from growing © 2014 Cengage Learning Engineering. All Rights Reserved.