Plastic deformation occurs above the yield stress by definition. In a tensile test at a given temperature, the strain rate is imposed and the stress and deformation (strain) vary. There is first an elastic (reversible) deformation under the yield stress and then a plastic (irreversible) deformation above the yield stress up to rupture. You can indeed encounter microplastic behaviour with local plastic deformation occurring at a stress under the global yield stress (of a test sample, in a component, etc.). But this is because the local stress is higher than the local yield stress.

Creep deformation can occur under the yield stress at a given temperature. In a creep test, the stress (or load) is imposed and the strain rate and deformation (strain) vary. In metals, after an instantaneous strain, the creep strain will show 3 stages called primary, secondary and tertiary creep. Tertiary creep ends with rupture. There is a threshold temperature for the full creep curve to be obtained. This temperature is around 0.4 Tm (Tm = melting temperature) with both temperatures in K. Below this temperature, only primary creep is observed. Above this temperature the three stages are observed up to rupture.

Hello Jingdong Hu,

please have a look on a similar question and  discussion

https://www.researchgate.net/post/How_to_calculate_the_threshold_stress_which_would_cause_creep_deformation

Dear Jingdong Hu, the answer on your question (yes or now) depends on the criteria  which introduced for the description of plastic flow initiating. Other words, what stress (local or microstress, equivalent stress or another superposition of stress components) are you taking into a mind in such description? 

Dear Serge V. Shil’ko, I mean in microstress. I guess if the dislocation energy (in forms of the Burger's Vector) is large enough, a microstress below the yield stress (since this stress often obtains from macrostructure tests) also can cause a plastic deformation in that dislocation area. Hence whether there is a criteria for microstructure plastic flow initiating? Thank you for your answering.

Dear Jingdong Hu,

Yes, there is such possibility for a plastic deformation belove the yield stress. This phenomenon is well known as "Microplasticity". For your information, please, see the paper by N. Brown "Observation of the mycroplasticity" in the book "Microplasticity". Ed. by C.J. McMahon, John Wiley & Sons, New York-London-Sydney.

In general,I would say yes.   plastic deformation can occur below the yield strength of materials.   This is because dislocation in the internal structures of solid polycrystallines can emerge to the free surfaces of the solid, causing micro-plastic deformation.   The fatigue phenomenon in solids is a good example  in which solid metals normally fail under the yield strength of the solid metals.

As mentioned in previous answers, I would say yes. Microplastic strains may occur at stresses below the yield point. These microplastic strains cannot be measured by common methods due to the discontinuity of their distribution and a varying character of their level in the metal structure. So it is hard to identify such microplastic deformation. But theses microplastic strains play a significant role in cyclic loading of metals (High cycle fatigue in specific).

One of the study to measure such microplastic strain for determining fatigue limit can be found below.

http://www.sciencedirect.com/science/article/pii/S1877705813019486

Creep is a plastic deformation which occurs below the yield stress but the condition is it is time dependent( will take years to fail) and it can happen only at high temperatures ( with respect to melting point of metal).

Plastic deformation occurs above the yield stress by definition. In a tensile test at a given temperature, the strain rate is imposed and the stress and deformation (strain) vary. There is first an elastic (reversible) deformation under the yield stress and then a plastic (irreversible) deformation above the yield stress up to rupture. You can indeed encounter microplastic behaviour with local plastic deformation occurring at a stress under the global yield stress (of a test sample, in a component, etc.). But this is because the local stress is higher than the local yield stress.

Creep deformation can occur under the yield stress at a given temperature. In a creep test, the stress (or load) is imposed and the strain rate and deformation (strain) vary. In metals, after an instantaneous strain, the creep strain will show 3 stages called primary, secondary and tertiary creep. Tertiary creep ends with rupture. There is a threshold temperature for the full creep curve to be obtained. This temperature is around 0.4 Tm (Tm = melting temperature) with both temperatures in K. Below this temperature, only primary creep is observed. Above this temperature the three stages are observed up to rupture.

The following paper is helpful:

A new view of the onset of plasticity during the nanoindentation of aluminium

By:Minor, AM (Minor, Andrew M.); Asif, SAS (Asif, S. A. Syed); Shan, ZW (Shan, Zhiwei); Stach, EA (Stach, Eric A.); Cyrankowski, E (Cyrankowski, Edward); Wyrobek, TJ (Wyrobek, Thomas J.); Warren, OL (Warren, Oden L.)

NATURE MATERIALS, Volume: 5, Issue: 9, Pages: 697-702.

Further, yield stress is defined as, in many situations, the stress level at 0.2% plastic deformation for the convenience of the measurement of the stress.

Mr.Jingdong H, 

Theoretically stress is proved to be in the regime of elastic deformation as per Hooke's Law.When it is given a peak value and when the things are no more elastic we have a liberty to allow a slight proportion of say up to 0.2%. When noticeably a stress make permanent state of material, we attribute it to plastic deformation. But initially the material is defensive against the stress caused by external load in any manner for smaller quantities not exceeding a fraction of the the elastic limit. It is fact that minimal deformation does occur which vanish with in fraction of seconds since the testing happened in the elastic regime. so we may consider the plus and minus strains to be equal take the state of material is as it was earlier to elastic loading. But minor plastic deformation enhanced by impact or creep may lead to a earlier yield point than expected in steady loading. Again it depends on the nature of loading and can not be generalised as purely elastic deformation for all loading conditions.

yes, time dependent creep deformation will happen even under very small loads. The book (can be accessed through the link below) by Ashby describes how it happens for different materials, loads temperatures etc

http://engineering.dartmouth.edu/defmech/

In fact the yield stress is not easy to define in some materials. If you take cubic face centred materails, you may not get a well defined yield point . The same is the case for some polymers and rubbers.

In metallic materails one talks of anelastic behavior at low stresses.

The phenomenon  of micro-plastic deformation in bulk (polycrystalline)  metals/alloys is a technological manifestation of imperfection  in which human  has not been able to develop a perfect bulk metals/alloys, thus far.   The imperfection of the bulk metals/alloys comprises not only dislocation lines, i. e., screw and edge dislocations, but also, imperfection points, i.e. substitutional and interstitial,as well as planar imperfections, i.e. stacking faults, and so.   All the above imperfections in bulk metals/alloys could contribute to the initiation of the micro-plastic deformation under the yield strength of the bulk metals/alloys, especially when the imperfections had the chance to emerge from the inner bulk to the free surface of the metals/alloys.   

I think I've found the answer from this article.

https://www.researchgate.net/publication/303958444_Quantification_of_dislocation_structures_from_anelastic_deformation_behaviour

Article Quantification of dislocation structures from anelastic defo...