6.10 Risk : structural and social

Structural risk is connected with individual and social risks. Individual risk is equal to structural risk times the number of structural elements and number of people at risk. The figure shows the structural and individual risks for a space shuttle. The individual risk of the crew member is the most important consideration, service with unacceptable individual risk (t > t₁) cannot be recommended. The more crew members, the higher the individual risk. If an oil pipeline passes near a settlement the structural risk for L kilometers of the pipeline is equal to L times the structural risk of one kilometer. The more people in the settlement, the bigger the individual risk. The structural risk of a severe accident of a structure can increase with time. If the risk exceeds the allowable value from corresponding industry standards the management of long-time service should be considered. Another situation where a unique engineering structure is assessed for safety and improvements were made in the structural elements. There are no severe accidents. Safety assessments, knowledge of the likelihood of failure scenarios, and the design improvement can decrease risk. The more knowledge the smaller the risk. The human factor plays a significant role. Nuclear power stations have backup systems and special nondestructive testing and inspections that decrease the risk. Statistics can help choose a profession with lowest risk. Fortunately, other factors such as salary and interest also affect the decision. Losses due to natural catastrophes such as tornadoes, earthquakes, forest fire, etc. at level 10¹⁰ are more valuable. More losses are connected with natural catastrophes than technical disasters.

References

Hahn G.J.,Shapiro S.S. Statistical Models in Engineering , John Wiley & Sons, 1994.

Kapur K.C. , Lamberson L. R. Reliability in Engineering Design , John Wiley & Sons, 1977.

Kumamoto H., Henley E.J. Probabilistic Risk Assessment and Management for Engineers , Inst of Electrical Engineers, 1996.

Madsen H.O., Krenk S., Lind N.C.Methods of Structural Safety, Prentice-Hall Inc., 1986.

Olkin I., Gleser L.J., Derman C.Probability Models and Aplications, Macmillan Publishing Co., Inc., 1980.

Tichy M. Applied Methods of Structural Reliability , Kluwer Academic Pub., 1993.

THEMES

Theme 1. Stress Concentration Theme 2. Fracure Mechanics Theme 3. Mechanical Properties Theme 4. Strength of Materials Theme 5. Theory of Elasticity Theme 6. Structural Safety Theme 7. Material Science Theme 8. Welds Theme 9.Composite Materials Theme 10. Finite Element Analysis

7 Materials science

Andrei Burov

7.1 Crystalline solids

The smallest repeating unit in a crystal is called the unit cell. The geometry and the position of the particles within the unit cell determine the structure of crystalline materials. Three edge lengths (a, b, c) and internal angles (a, b, g) will be used to describe the geometry of a unit cell. There are seven crystal systems and fourteen possible unit cells (Bravais unit cells) depending on the values of a, b, c and a, b, g. Some of the particles within a unit cell may be shared and therefore do not belong completely to an individual cell. Therefore, in order to calculate number of particles per unit cell we have to consider the following contributions for each particle according to its position: - atoms centered on the face count 1/2; - atoms centered on the edge count 1/4; - atoms centered on the vertex count 1/8 In a simple cubic number of atoms per unit cell = 1; in a body centered cubic - 2; in a face centered cubic - 4. Atomic packing factor = (Volume of atoms)/(Volume of unit cell). For a simple cubic - atomic packing factor = 0.52; a body centered cubic - 0.68; a face centered cubic - 0.74 To determine a crystallographic direction [uvw] in a unit cell: 1. Find the vector projections on the three axes. A - 1,0,1; B - 0,1/2,1; C - 0,1,1/2; D - 1/2,1,0; E - 1,1,0; F - 1,1/2,0. 2. Reduce these coordinates to the 3 smallest integers having the same ratio. A - [101]; B - [012]; C - [021]; D - [120]; E - [110]; F - [210]. A plane within a crystal is defined by the Miller indices. To determine crystallographic (Miller) indices (hkl) of the plane: 1. Find intercepts of a plane on the three axes in terms of the unit cell dimensions. 2. Determine the reciprocals of these numbers. 3. Reduce the reciprocals to the three smallest integers. There are two main types of planar defects called dislocations - edge dislocation and screw dislocation. A dislocation is a sharp change in the order of atoms along a line. Dislocations move on the slip plane. The magnitude and direction of the slip is defined by the Burger's vector, b. For an edge dislocation the direction of slip is perpendicular to the direction of the dislocation. For a screw dislocation the direction of slip is parallel to the direction of the dislocation. Slip is known to occur on planes (shown on the picture) in the direction of the maximum density of atoms. This is called a slip system. If there are many slip systems then deformation can occur relatively easily and the metal is considered ductile. BCC crystal structure has up to 48 slip systems. FCC crystal structure has 12 slip systems. HCP crystal structures have only 3 slip systems. Accordingly, most metals with a HCP crystal structure (Mg, Zn, Be) are less ductile than metals with a BCC (W, Fe, K) or FCC (Cu, Al, Ni) structure. The distance between atoms varies depending on the crystallographic directions. This is the cause of the anisotropy of mechanical and physical properties of a crystal. Therefore, samples cut from a monocrystal in different directions will exhibit a difference in the stiffness. In the FCC and BCC crystals of metals the highest elastic modulus is found in [111] direction, while the lowest is found in the direction of [100]. Real materials consist of many chaotically oriented monocrystals, which results in the isotropy of their properties. Some materials can exist with different crystal structures. This can be demonstrated by pure iron which has a body centered cubic (BCC) structure at room temperature and a face centered cubic (FCC) structure at 911 _oC. This change is accompanied by shrinkage in volume due to the FCC structure being more closely packed than the BCC structure. The second transformation of crystal structure from FCC to BCC occurs at 1392 _oC.