physics

Hill yield criterion

Hill yield criterion is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hill yield criterion rather than just read about it. In short: The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations. The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form.

Key takeaways

Hill yield criterion belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hill yield criterion to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hill yield criterion from memory before moving on to harder problems.

Reference excerpt

The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations. The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form. This model was later generalized by allowing for an exponent m. Variations of these criteria are in wide use for metals, polymers, and certain composites.

Quadratic Hill yield criterion The quadratic Hill yield criterion has the form :

F ( σ 22 − σ 33 ) 2 + G ( σ 33 − σ 11 ) 2 + H ( σ 11 − σ 22 ) 2 + 2 L σ 23 2 + 2 M σ 31 2 + 2 N σ 12 2 = 1 . {\displaystyle F(\sigma _{22}-\sigma _{33})^{2}+G(\sigma _{33}-\sigma _{11})^{2}+H(\sigma _{11}-\sigma _{22})^{2}+2L\sigma _{23}^{2}+2M\sigma _{31}^{2}+2N\sigma _{12}^{2}=1~.}

Here F, G, H, L, M, N are constants that have to be determined experimentally and σ i j {\displaystyle \sigma _{ij}} are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent. It predicts the same yield stress in tension and in compression.

Expressions for F, G, H, L, M, N If the axes of material anisotropy are assumed to be orthogonal, we can write

( G + H ) ( σ 1 y ) 2 = 1 ; ( F + H ) ( σ 2 y ) 2 = 1 ; ( F + G ) ( σ 3 y ) 2 = 1 {\displaystyle (G+H)~(\sigma _{1}^{y})^{2}=1~;~~(F+H)~(\sigma _{2}^{y})^{2}=1~;~~(F+G)~(\sigma _{3}^{y})^{2}=1}

where σ 1 y , σ 2 y , σ 3 y {\displaystyle \sigma _{1}^{y},\sigma _{2}^{y},\sigma _{3}^{y}} are the normal yield stresses with respect to the axes of anisotropy. Therefore, we have

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Hill yield criterion

Start with the simplest possible case. Write down what Hill yield criterion claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hill yield criterion before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hill yield criterion ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hill yield criterion

In research: Hill yield criterion appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hill yield criterion in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hill yield criterion is common in secondary-school and first-year university syllabi. It links to neighbouring topics Plasticity (physics), Yield criteria, so understanding it makes those chapters shorter.
In everyday life: Look for Hill yield criterion outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hill yield criterion in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hill yield criterion means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hill yield criterion out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hill yield criterion in simple terms?

Why does Hill yield criterion matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hill yield criterion?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hill yield criterion.