MSE306Chap3Bonding

MSE306Chap3Bonding - Class Business Return HWK#1 Solutions...

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Class Business Return HWK #1 Solutions available in my office Please review your problem areas in preparation for the exams Toolkit homepage will be set up today or tomorrow: schedule, assignments, and some lecture notes will be posted. In terms of priority, please read text first, then refer to lecture notes HWK #2 will be posted to web Will be due next Thursday Solutions will be available at the same time The problems will outline scope of exam the following Thursday
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Bonding Introduction Our interest in all the structural concepts introduced during this course (including bonding) is properties. I presume you all have been introduced to the basics in previous Chemistry, Physics, or Materials courses (consider this review) I will attempt to outline clear connections between the nature of bonds and properties. Generally, the examples are mechanical due to my own bias, as well as that of the text I will also reemphasize anisotropy So…let’s take a step back and review the basics of stress and strain This information will be CRITICAL in Chap. 4, and it is assumed prerequisite knowledge for this course so review it personally in
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Average Stress and Strain Stress Strain Material’s response to applied load Is it a mathematical construct? How do we measure it? State Variable Geometry of deformation It is real, measurable? Not generally a State Variable P dA σ P A P A dA dA = = = 0 0 0 0 L L L L L L e - = = = δ L o δ
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Tensors J.F. Nye from Chapters 1& 2 Meyers & Chawla, Chapter 1, Part B Dieter, Chapter 2 density = mass/volume all scalar quantities current = conductivity x electric field current and field are vectors, what about conductivity? For this class, the mathematics of tensors is not required, however, we introduce the concept .
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Using conductivity as an example: Ohm’s Law states that the current density, j , passing through a material is proportional to the applied field, E . The proportionality constant is the material’s conductivity. We frequently think of all these quantities as scalars. Conductivity is a 2nd rank tensor relating 2 vectors (or 1st rank tensors). What would the values of σ be for isotropy? If my reference coordinate system changes, how does the material property change? How do the tensor components change? Tensors (change of basis) 3 13 2 12 1 11 1 E E E j E j j ij i σ + σ + σ = σ = σ = E j Isotropy Anisotropy E E j j
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Tensors (introduction) Scalar - magnitude Rank 0 1 component speed, temperature, pressure Vector - magnitude and direction Rank 1 3 comps. each associated with basis directions force Tensor 2nd rank - Rank 2 9comps. each associated with a pair of directions in a set order stress, strain properties relating a scalar and 2nd rank tensor thermal expansion: temperature and strain Tensor 3rd rank - Rank 3 properties relating a vector and 2nd rank tensor piezoelectric effect: current and strain or stress Tensor 4th rank - Rank 4
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MSE306Chap3Bonding - Class Business Return HWK#1 Solutions...

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