Compute creep strain and stress relaxation in real time via the Norton power law ε̇=Aσⁿexp(-Q/RT). Select 316SS or IN718 presets, adjust temperature, and visualize Arrhenius-corrected multi-temperature curves.
Material & Mode
Norton Constants
Stress exponent n
Activation energy Q (kJ/mol)
kJ/mol
Loading Conditions
Stress σ₀ (MPa)
MPa
Temperature T (°C)
°C
Elastic modulus E (GPa)
GPa
Time range t_max (h)
h
Summary
Results
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έ̇ (s⁻¹) at T,σ
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Time to ε=1% (h)
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σ(t_max) MPa
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T/Tm (homologous)
① Creep Strain ε(t) vs Time
Creep
② Stress relaxation σ(t) - multiple temperatures (T₀, T₀+100K, T₀+200K)
$$\sigma(t) = \frac{\sigma_0}{\left[1 + E A n \sigma_0^{n-1}t\right]^{1/n}}$$
What is Creep & Stress Relaxation?
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What exactly is "creep"? I've heard metals can slowly deform over time, but that sounds weird for a solid.
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Basically, creep is the slow, permanent deformation of a material under a constant stress, even if that stress is below its yield strength. It's a time-dependent process that becomes really important at high temperatures. For instance, a turbine blade in a jet engine is under huge stress and heat; over thousands of hours, it can slowly stretch. Try moving the "Temperature" slider in the simulator above to 700°C for IN718 and see how the creep strain curve shoots up.
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Wait, really? So if creep is constant stress, what's "stress relaxation"? They sound opposite.
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Great question! They're two sides of the same high-temperature phenomenon. In stress relaxation, the strain is held constant. Initially, you stretch a bolt to a certain length (strain), which creates a high stress. Over time, due to creep mechanisms, that stress relaxes or decreases, even though the length hasn't changed. A common case is a bolted joint in a hot engine—it can loosen over time because the clamping force (stress) drops. In the simulator, switch the view to "Stress Relaxation" to see the stress drop from its initial value over time.
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That makes sense. So what do the "Stress Exponent n" and "Activation Energy Q" sliders actually control in the metal's behavior?
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Those are the key material properties in the Norton power law. `n` tells you how sensitive the creep rate is to stress. A high `n` (like 8 for IN718) means a tiny increase in stress causes a massive jump in creep rate—it's very non-linear. `Q` is the energy barrier for atoms to move and cause creep; a higher `Q` means creep is more strongly suppressed by temperature. Play with it: set a high `n` and watch the curve bend sharply, or increase `Q` and see how much you have to raise the temperature to get the same creep effect.
Physical Model & Key Equations
The simulator uses the Norton Power Law (Secondary Creep Law) to model the steady-state creep strain rate. This equation captures how the rate depends on applied stress and temperature.
Where:
• $\dot{\varepsilon}_{cr}$: Steady-state creep strain rate (1/s)
• $A$: Material constant (pre-exponential factor)
• $\sigma$: Applied stress (MPa)
• $n$: Stress exponent (unitless, from slider)
• $Q$: Activation energy for creep (J/mol, from slider)
• $R$: Universal gas constant (8.314 J/mol·K)
• $T$: Absolute temperature (Kelvin = °C + 273.15)
The exponential term $\exp(-Q/RT)$ is the Arrhenius factor, governing the dramatic effect of temperature.
For stress relaxation, we assume the total strain (elastic + creep) is constant. As creep strain increases, elastic strain must decrease, which in turn reduces the stress. Solving this condition gives the stress as a function of time.
$$\sigma(t) = \frac{\sigma_0}{\left[1 + E A n \sigma_0^{\,n-1}t \exp\!\left(-\frac{Q}{RT}\right) \right]^{1/n}}$$
Where:
• $\sigma(t)$: Relaxing stress at time $t$ (MPa)
• $\sigma_0$: Initial stress (MPa, from slider)
• $E$: Elastic modulus (GPa, from slider)
• $t$: Time (hours)
• Other terms as defined above.
This equation shows how the initial stress $\sigma_0$ decays over time. The rate of decay depends critically on $E$, $n$, and the temperature through the exponential term.
Frequently Asked Questions
By manually inputting the material constant A, stress exponent n, and activation energy Q, any material can be supported. Please set each parameter with reference to literature values or experimental data.
Creep strain is the strain that increases over time under constant stress. Stress relaxation is a phenomenon where stress decreases when a constant strain is maintained. This tool calculates and visualizes both in real time based on Norton's law.
When the temperature is changed, the exp(-Q/RT) term in Norton's law is automatically calculated, and the creep rate changes exponentially. The higher the temperature, the easier it is to overcome the activation energy barrier, and the strain rate increases.
Since Norton's law only describes steady-state creep, errors occur in the primary creep and tertiary creep regions. Additionally, the power law may break down in high-stress regions, so please check the applicable range before use.
Real-World Applications
Jet Engine & Gas Turbine Blades: These components operate under extreme centrifugal stress and temperatures over 1000°C. Creep deformation limits their service life. Engineers use models like the Norton law to predict blade elongation and prevent catastrophic failure, scheduling maintenance based on calculated creep life.
Nuclear Reactor Components: Fuel cladding, heat exchangers, and pressure vessels are subjected to high temperature, stress, and radiation for decades. Stress relaxation in bolts and fasteners must be accounted for to maintain structural integrity and leak-tightness over the plant's lifetime.
Power Plant Steam Pipes: Superheated steam pipes carry high-pressure steam at temperatures where creep is significant. Engineers monitor creep strain to schedule pipe replacement before wall thinning leads to rupture, ensuring plant safety and preventing unplanned outages.
Electronic Solder Joints: Even at relatively low "room temperature," the homologous temperature for solder is high. Under constant stress from thermal expansion mismatches, solder joints can creep, leading to eventual electrical failure in circuits. This is a key reliability concern in microelectronics.
Common Misunderstandings and Points to Note
When you start using this simulator, there are a few points that are easy to stumble on, especially for CAE beginners. First and foremost, keep in mind that Norton's Law is not a universal solution. This equation primarily describes the region known as "steady-state creep (secondary creep)". Real materials also include initial "primary creep" and "tertiary creep" just before rupture, so consider this tool's results as indicative of steady-state tendencies. For instance, if you need to precisely predict strain after 1000 hours, you often need to separately account for the contribution of primary creep.
Next, handling the material constants (A, n, Q). The preset values are representative, but even for the same "316SS", the numbers can vary based on manufacturing lot or heat treatment history. When using it for actual design work, the golden rule is to use constants you've fitted yourself from measured data of the target material. Also, while the temperature dependence is corrected by the Arrhenius term, it's easy to forget that Young's modulus E also decreases with temperature. In this simulator, E is fixed, but in actual stress relaxation calculations, if you don't use the E value corresponding to the operating temperature, you'll underestimate the relaxation rate, so be careful.