# Creep (materials)

Creep (also retardation ) refers in materials time- and temperature-dependent viscoelastic or plastic deformation under constant load. A measure of the creep is the creep or the creep value ( English creep coefficient ).

Creep has to be taken into account in constructional tasks such as mechanical engineering or in civil engineering and influences the behavior of the respective objects e.g. T. to a considerable extent. Depending on the material, mechanical tension, durability, risk of damage, application, these effects can sometimes be neglected in the course of engineering precision. It generally applies to all metallic materials as well as to polymers ( plastics , rubber ) and a number of ceramics, including concrete, but also to wood and snow .

## Creep in concrete

Creep is the increase in deformation of the concrete over time under constant stress. It is a property of concrete that manifests itself, especially when the pressure load is used to a high degree, through a structural transformation and a reduction in volume.

Creeping is made possible by the water contained in the cement stone . An external load leads to a change of place of water molecules in the cement stone gel. In addition, there are compression and sliding processes between the gel particles. Chemically unbound water is pressed from the cement pores into the capillaries and evaporates, which causes the gel to shrink. The increase in creep deformations becomes less and less over time and only comes to a standstill after several years.

Creep is made up of two parts. The reversible deformation component , which decreases with a time delay after the load is removed , also known as creep back , is little influenced by the age of the concrete and reaches its final value after a short time. The dominant irreversible deformation component remains fully intact after the load is removed ; it is also referred to as flow , but is heavily dependent on the age of the concrete and only reaches its value after a long time. Under unfavorable boundary conditions, the final creep index can reach a value of approximately 3.0, i.e. H. the concrete deformations due to creep are three times as large as from the elastic deformation.

The course and extent of creep are influenced not only by the size of the load and the age of the concrete, but also by the cement stone volume and the water-cement value . Further parameters are humidity , cross-sectional geometry of the component, hardening speed of the cement and concrete compressive strength . The creep coefficients are determined in the laboratory using the creep test.

The information in DIN 1045-1 applies to linear creep under compressive stress, i.e. H. the creep coefficients are independent of the load level. This applies up to a tension of approximately 45% of the cylinder strength of the concrete. At higher concrete compressive stresses, non-linear creep occurs as a result of increased microcrack formation in the concrete. The creep deformations increase disproportionately with increasing load.

When calculating prestressed concrete parts ( prestressed concrete ), the creep of the concrete is an important parameter that must be taken into account, as the prestressing generally introduces large compressive concrete stresses. The resulting creep compression of the concrete component reduces the prestressing steel strain and thus also the prestressing force. However, the creep of the concrete can also be decisive in the verification of the load-bearing capacity of slender reinforced concrete columns or in the verification of deformation of slender ceilings .

Creep should not be confused with concrete shrinkage , which is the reduction in volume due to moisture loss in the concrete.

## Creep in plastics

Since plastics consist of large (in the case of thermoplastics and elastomers, tangled) molecular chains, these slide or untangle under external stress, which results in elongation. Depending on the manufacture, base polymer, filler and degree of filling of the plastic, the elongation can be several 100%.

## Creep in metallic materials

The properties of metallic materials are time-dependent above a transition temperature , since all structural mechanisms are thermally activated here. The transition temperature depends on the material and is around 30% to 40% of the melting temperature in Kelvin. At these high temperatures ( ), a number of different changes in the state of the material take place, which can be traced back to the effects of temperature, mechanical stress, time and the ambient atmosphere. Here, metallic materials undergo irreversible plastic deformation, even with low mechanical stresses below the yield point , which progresses slowly but steadily. This advancing plastic deformation under static load is called creep and is temperature, stress, time and material dependent. Creep is always associated with damage to the metallic material. Creep is essentially based on transcrystalline processes such as dislocation movements and vacancy diffusion. But intergranular processes such as grain boundary sliding and grain boundary diffusion are also involved in creep. ${\ displaystyle T_ {t}}$${\ displaystyle T> T_ {t}}$ ${\ displaystyle R_ {e}}$

While a static load below the yield point generally only leads to elastic deformation at room temperature and can be endured by components for practically an indefinite period of time, creep under high temperature stress leads not only to elastic elongation but also to plastic elongation (creep elongation) that progresses over time material damage is associated and the component life is limited. A distinction is made here (with increasing load):

The different creeping mechanisms occur side by side and coupled one after the other. Diffusion creep occurs independently of the other processes, so that the fastest process in each case determines the creep speed. The other mechanisms are coupled with one another so that the slowest process determines the creep speed.

Creep leads to a reduction in strength values, the dependence of which on the parameters temperature, mechanical stress, time and material is very complex. Creep during high temperature stress is a significant problem in the art as it can lead to component failure , e.g. B. by collision of turbine blades on the housing, change in shape of highly stressed notches on turbine shafts or leakage of boiler tubes. Knowledge of the material's creep behavior under operational stress is therefore essential for the design and operation of high-temperature components. Creep cannot be prevented when exposed to high temperatures. However, the creep process can be influenced by targeted alloying measures. This is why special materials (e.g. martensitic and austenitic steels or nickel-based alloys ) are used for high-temperature components.

Creep test for metallic materials

The creep behavior is determined with so-called creep tests (standardized according to DIN EN 10 291 and ISO 204). In the creep test, a sample is statically loaded at a constant high temperature and the elongation of the sample due to plastic deformation is measured over time. The creep strain can be determined from this plastic deformation. This results in the creep curve shown in the picture, which is divided into the technical creep areas I, II and III.

Creep curve and structural processes during a creep test

Another important result of the creep test is the stress time until breakage . Creep tests at different mechanical stresses result in different stress times before breakage. The creep strength determined from this is essential for the design of components . The creep rupture strength is the stress that the material can withstand at that temperature for the period of stress until failure. The technically relevant exposure times are often several years, so that creep tests are usually carried out for a very long time. ${\ displaystyle t_ {u}}$ ${\ displaystyle R_ {u, t, T}}$${\ displaystyle T}$${\ displaystyle t}$

### Mathematical description

Norton's law of creep is often used for the mathematical description of the area of ​​almost constant creep rate (secondary creep) . From investigations into the secondary creep range, Norton developed a first purely stress-dependent creep description in 1929, which describes the minimum creep speed as a power function of the stress:

${\ displaystyle {\ dot {\ varepsilon}} _ {\ mathrm {min}} = K \ cdot \ sigma ^ {n}}$

The stress exponent and the factor represent temperature-dependent material constants. The stress exponent is also an indicator for the deformation mechanism. In the literature, dislocation creep and grain boundary slip are assumed for a stress exponent. At very low stresses or creep speeds, stress exponents of can occur, which describe the deformation mechanism based exclusively on diffusion creep . Norton's law of creep is still in use today because of its simple applicability and is used for a rough estimate of creep deformations or stress redistributions as well as stress relaxation in the component. However, it is only valid for medium and low voltages in the secondary creep range and an identification of the parameters and must be carried out separately for each application temperature. ${\ displaystyle n}$${\ displaystyle K}$${\ displaystyle n}$${\ displaystyle n = 4 \ ldots 7}$${\ displaystyle n = 1 \ ldots 2}$${\ displaystyle n \ approx 1}$${\ displaystyle K}$${\ displaystyle n}$

Much more powerful descriptions are required for more precise calculations of time and temperature-dependent deformations at high temperature loads. A distinction is made here between phenomenological equations, which represent mathematical descriptions of the measured creep curves, and constitutive equations, which are based on continuum mechanical or microstructural approaches and couple deformation and damage. One powerful type of equation provides e.g. B. the phenomenological "modified Garofalo equation" or the constitutive "Chaboche model". Both types of descriptions are usually very time-consuming to identify parameters and require a great deal of mechanical and material knowledge.

### Light metal alloys

In light metal alloys such as aluminum and magnesium alloys, which are often used in vehicle and aircraft construction, creep occurs at temperatures of approx. 50-100 ° C. The increased number of slip planes in the face-centered cubic crystal structure of aluminum also offers less resistance to the plastic creep deformation process, which limits the use of these alloys for elevated temperatures.

### Prestressing steel

In the case of high-strength prestressing steels , creep is also possible at room temperature and at high, constantly acting service stresses below the yield point. Their use for prestressing prestressed concrete structures causes creep strain and thus stress losses as a result of relaxation (decrease in stress at constant strain). These voltage losses can be up to 10% of the initial voltage.

## Creep on floors

Soils deform over time under compressible and shearing loads. On the one hand, consolidation occurs, in which cohesive , poorly permeable soils absorb or release the pore water only with a time delay; on the other hand, creep plays an important role due to the viscosity of the soil.

In the case of compressible stresses under one-dimensional (oedometric) or hydrostatic ( isotropic ) stresses , the density of a floor element increases further under constant effective stresses. The increase in density follows the following empirical law for one-dimensional compression:

${\ displaystyle \ varepsilon _ {cr} = C_ {a} (1-e_ {0}) \ cdot \ log (t / t_ {0})}$

With

• ${\ displaystyle \ varepsilon _ {cr}}$ the one-dimensional elongation due to creep
• ${\ displaystyle C_ {a}}$an empirical creep coefficient
• ${\ displaystyle e_ {0}}$the initial number of pores
• ${\ displaystyle t_ {0}}$ a reference time.

## semantics

The meaning ( semantics ) of the term creep is often used very vaguely in technical practice and is often equated with the term relaxation . A simplified distinction is possible through:

• Creep : constant tension , increasing elongation as a function of time,
• Relaxation : constant elongation, decreasing tension as a function of time.

## Individual evidence

1. Fritz Röthemeyer, Franz Sommer: Rubber technology . 2nd Edition. Carl Hanser Verlag, Munich / Vienna 2006, pp. 514-515, ISBN 978-3-446-40480-9 .
2. J. Rösler, H. Harders, M. Bäker: Mechanical behavior of materials . Springer, 2006, p. 383.