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Polymers. Image Credit: Shutterstock.com/Meaw_stocker

Nabarro-Herring Creep: Definition, How It Occurs, Factors, and Importance in Manufacturing

Xomety X
By Team Xometry
July 28, 2023
 9 min read
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Nabarro-Herring creep, also known as volume diffusion-controlled creep, is a phenomenon that occurs in crystalline and amorphous materials when subjected to high temperatures and low but constant mechanical stresses. Nabarro-Herring creep is exclusively governed by the diffusion of mass within the material. This type of creep develops when vacancies diffuse from grain boundaries that have high chemical potential and experience tensile stresses toward grain boundaries that have low chemical potential and experience no tensile stresses. Temperature, stress, grain size, and material composition are all factors that can affect this kind of creep. An understanding of Nabarro-Herring creep is essential when designing parts that must withstand high temperatures and prolonged loading conditions without deforming or failing during the manufacturing process. This article will discuss Nabarro-Herring creep, how it occurs, the factors that affect it, and the role it plays in the manufacturing process.

What Is Nabarro-Herring Creep?

Nabarro-Herring creep is a type of creep deformation that happens in materials at high temperatures under a constant load. In general, creep describes the gradual and time-dependent deformation of materials that remain under prolonged stress of some kind. The primary mechanism of deformation in Nabarro-Herring creep is atom diffusion within the material. It is possible to explain the yielding of a polycrystalline solid under shearing stress by self-diffusion taking place within the grains. Each crystal grain experiences a diffusion-driven flow of matter within its structure. Atoms slowly move toward boundaries with normal tension and away from boundaries experiencing normal pressure. The creep strain is a result of atom migration. The diffusion of atoms plays a crucial role in this type of creep, contributing to the gradual deformation observed in the material. For more information, see our guide on Material Creep.

Figure 1 is a schematic diagram of Nabarro-Herring creep:

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Nabarro-Herring Creep
Nabarro-Herring Creep
Nabarro-Herring Creep

Nabarro-Herring Creep.

Image Credit: https://www.researchgate.net/

How Does Nabarro-Herring Creep Occur?

Bulk diffusion is the mechanism that drives Nabarro-Herring creep. In the vicinity of grain boundaries at high temperatures, vacancies (empty lattice sites) tend to accumulate perpendicular to the applied stress rather than in the parallel direction. Because of the uneven distribution of vacancies, the grain boundaries experience a gradient of such diffusion, which, in turn, encourages atom migration. As a result, the material displays creep deformation in which it gradually elongates or deforms under constant applied stress.

What Are the Factors of Nabarro-Herring Creep?

The factors that lead to Nabarro-Herring creep are listed below:

  1. Temperature: The creep rate increases with higher temperatures due to enhanced atomic diffusion.
  2. Grain Size: Fine-grained materials exhibit higher creep rates because each grain can experience its own grain boundary diffusion.
  3. Strain Rate: Higher strain rates can accelerate creep deformation.
  4. Environment: Corrosive agents or reactive atmospheres can affect creep by accelerating diffusion processes.

These factors collectively influence the Nabarro-Herring creep behavior of a material, determining its resistance to deformation under constant stress over time.

When Was Nabarro-Herring Creep Proposed?

Nabarro proposed the Nabarro-Herring creep mechanism in 1948, and Herring expanded on it in 1950. According to the mechanism, creep in a polycrystalline solid can happen at low-stress levels through diffusional flow along grain boundaries rather than only as dislocation motion. The phenomenon was then named for the two primary researchers who described it.  

According to the mechanism, when a polycrystalline material experiences low applied stress, atoms can diffuse along the grain boundaries from compression-prone regions to tension-prone ones. Creep deformation occurs as a result of this diffusional flow even when there’s no dislocation motion. In materials with small grain sizes, where the contribution of grain boundary diffusion becomes more significant, the Nabarro-Herring creep mechanism is particularly significant. 

How Does Nabarro-Herring Creep Compare to Coble Creep?

Both Coble creep and Nabarro-Herring creep are characterized by the diffusion of atoms along grain boundaries within a material. They also both exhibit a linear relationship between the strain rate and the applied stress (σ). This means that the strain rate increases with increasing stress. However, there is a difference in the relationship between the strain rate and the grain size (d). In Coble Creep, the strain rate is inversely proportional to the cube of the grain size (d³). In contrast, in Nabarro-Herring Creep, the strain rate is inversely proportional to the square of the grain size (d²).

How Is the Nabarro-Herring Creep Rate Derived?

Analyzing the behavior of a single rectangular grain in a polycrystalline material allows for the derivation of the Nabarro-Herring creep rate equation. This equation takes into account the change in volume that results from applying compressive and tensile stresses to opposing sides of the grain. The equation accounts for vacancy flux by looking at the concentration of vacancies in the compressive and tensile regions. The equation takes into account several variables, including temperature, grain size, vacancy diffusivity, vacancy motion, and formation energies. The equation, when reduced to its simplest form, connects the Nabarro-Herring creep rate to the lattice self-diffusion coefficient, grain size, stress, atomic volume, and temperature. The equation for the creep rate in Nabarro-Herring creep is given as:

ε =A (D * b³) / (k * T) * (σ / ρ) * (d-2)

Where:

ε = creep rate

D =  diffusion coefficient

b =  Burgers vector magnitude

k =  Boltzmann's constant

T =  absolute temperature

Σ =  applied stress

ρ =  density of dislocations

d =  grain size

This equation shows that the creep rate is proportional to the diffusion coefficient, applied stress, and the inverse square of the grain size.

What Is the Importance of Nabarro-Herring Creep in Manufacturing Process?

Nabarro-Herring creep has significant effects on material behavior and reliability which makes it important in manufacturing. It is essential to comprehend and account for Nabarro-Herring creep to avoid creep failure in parts and structures exposed to high temperatures and sustained stresses.

Creep failure can happen when materials gradually elongate and deform over time while being subjected to a constant load. They eventually lose their structural integrity and dimensional stability. Engineers can accurately estimate creep strain and forecast the lifetime of components by taking Nabarro-Herring creep into account when designing components and choosing materials. This information lets them create reliable manufacturing procedures and choose materials with appropriate creep resistance, ensuring the reliability and longevity of products.

How Can Nabarro-Herring Creep be Prevented?

Preventing Nabarro-Herring creep depends upon your ability to minimize atomic diffusion and grain boundary sliding. Some effective approaches include:

  1. Material Selection: Choose materials with higher melting temperatures and better creep resistance, such as advanced alloys or ceramics.
  2. Alloying and Microstructural Engineering: Add alloying elements or heat-treat the material to make the microstructure more creep-resistant. 
  3. Stress Management: Avoid excessive stress levels and apply stress-relieving techniques to eliminate creep’s driving force. 
  4. Temperature Control: Operate within acceptable temperature ranges and minimize exposure to elevated temperatures. 

Does Nabarro-Herring Creep Only Occurs on Polymers?

No, Nabarro-Herring creep can occur in many materials, including metals, ceramics, and polymers. It refers to the time-dependent deformation of a material under a constant load or stress, usually at elevated temperatures.

The temperature range at which Nabarro-Herring creep becomes significant varies depending on the material. For metals, creep is typically observed at temperatures above 0.3 to 0.4 times their melting point (in absolute temperature). In the case of polymers, creep can occur at lower temperatures due to their low melting points and low mechanical strength values. Nabarro-Herring creep can be relevant in various materials, particularly crystalline materials where the diffusion of atoms along dislocation lines or grain boundaries plays a significant role in the deformation process.

For more information, see our guide on What Are Polymers.

Is Nabarro-Herring Creep Caused by High Temperature?

Yes, Nabarro-Herring creep is partially caused by high temperatures. This phenomenon occurs specifically at elevated temperatures, often at or above 0.4 times the material's melting temperature. The other causal factor is applied stress. Nabarro-Herring creep is only one type of creep in crystalline materials. It involves the diffusion of atoms through the crystal lattice, leading to the gradual rearrangement of crystal defects and resulting in macroscopic deformation over time.

At high temperatures, atoms have sufficient thermal energy to overcome energy barriers and move within the material. Nabarro-Herring creep specifically occurs when the diffusion of vacancies and interstitials contributes significantly to the material's deformation under applied stress.

Is Nabarro-Herring Creep Safe?

No, Nabarro-Herring creep is not safe. All types of creep pose potential risks to the structural integrity of materials. Over time, the deformation caused by Nabarro-Herring creep can lead to dimensional changes, distortion, and even failure of the material under constant load or stress.

Creep is particularly concerning in engineering applications where long-term stability and reliability are crucial, such as high-temperature components in power plants and aircraft. The gradual deformation can compromise the structural integrity, leading to catastrophic failures. To ensure safety, engineers and materials scientists must carefully consider the creep behavior of materials and design structures with appropriate allowances, materials, and operating conditions to mitigate potential risks.

What Is the Difference Between Nabarro-Herring Creep and Dislocation Creep?

The fundamental deformation mechanisms distinguish Nabarro-Herring creep from dislocation creep. Dislocation creep involves the motion of dislocations within the crystal lattice as the predominant mechanism for deformation under stress, whereas Nabarro-Herring creep is primarily controlled by the diffusion of vacancies.

Summary

This article presented Nabarro-Herring creep, explained it, and discussed how it occurs. To learn more about Nabarro-Herring creep, contact a Xometry representative.

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Xomety X
Team Xometry
This article was written by various Xometry contributors. Xometry is a leading resource on manufacturing with CNC machining, sheet metal fabrication, 3D printing, injection molding, urethane casting, and more.