A specimen \(1015 \mathrm{mm}\) (40 in.) long of a low carbon-nickel alloy (Figure 8.31 ) is to be exposed to a tensile stress of \(70 \quad \mathrm{MPa}\) \((10,000 \mathrm{psi})\) at \(427^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right) .\) Determine its elongation after 10,000 h. Assume that the total of both instantaneous and primary creep elongations is \(1.3 \mathrm{mm}(0.05 \text { in. })\)

When materials are subjected to a constant load or stress over an extended period, they undergo a phenomenon known as 'creep', which is the time-dependent and progressive deformation under constant stress. Specifically, the secondary creep rate refers to the steady-state stage where the rate of deformation is constant over time. Creep behavior is often divided into three stages: primary creep, secondary creep, and tertiary creep.

In the context of the exercise solution provided, the secondary creep rate is critical for predicting the long-term behavior of materials under stress. To calculate the secondary creep elongation (L_s), one needs the secondary creep rate (ε), the original length L), and the time (t) the material has been under load. The relationship is given by the formula: L_s = ε x L x t), where ε is expressed in inverse seconds (s^-1).

In real-world applications, understanding the secondary creep rate allows engineers to predict how much deformation a material will experience over the lifecycle of a structure or component, thus ensuring safety and functionality.

Tensile stress is a fundamental concept in material science and engineering, referring to the force per unit area within materials that arises from externally applied forces. It is calculated by dividing the force applied by the cross-sectional area that is perpendicular to the force. The unit of tensile stress is the Pascal (Pa), with 1 Pa equivalent to 1 Newton per square meter.

In our textbook example, the tensile stress applied to a low carbon-nickel alloy was 70 MPa, which is a substantial amount of force that could lead to significant deformation of the material over time. The effects of tensile stress are not instantaneous; some materials can stretch or elongate significantly before reaching their breaking point. The elongation experienced by the alloy in the exercise helps in predicting the material's behavior under long-term load conditions, which is essential in design and failure analysis.

Material deformation refers to the change in shape or size of a material when subjected to an external force. There are various forms of deformation, such as elastic, plastic, and viscous deformation, each characterized by their response to stress. Elastic deformation is temporary and reversible, plastic deformation is permanent, and viscous deformation, typically found in fluids, depends on the rate of applied stress.

In relation to the exercise, the total elongation of the material after a specified period includes immediate, or 'instantaneous' deformation, followed by primary and secondary creep. Instantaneous deformation occurs as soon as the stress is applied, whereas primary creep happens in the period shortly after, before the material enters the secondary creep phase. The combined understanding of these deformation processes provides a comprehensive overview of how materials will respond under various loading conditions, which is indispensable for creating safe and reliable designs in engineering and construction.