1. ・A new mechanical condition-based maintenance technology is proposed through the use of instrumented indentation technique. In the proposed techniques, the true stress-strain curve of material can be obtained by using spherical indenter and the residual stress of material by Vickers and Knoop indenters. The instrumented indentation technique is not nondestructive but semi-nondestructive, which involves a very small blemish. However, it is expected to be useful for, including but not limited to, as an ISI technique depending on objects.

1. ・In the instrumented indentation technique, a continuous curve of indentation load vs. indentation depth is obtained (Fig. 1).
   
   
   

1. ・ In the spherical indentation, the representative stress (σ_r) - strain (ε_r) relation are determined at the different strain levels according to indentation depth by the following equation
   
   　　　　 σ_r = (1/Ψ)(L/πa²)
   　　 　　ε_r = 0.14(a/R){1-(a/R)²}^-1/2

1. ・ where, Ψ : constraint factor, L : indentation load, a : contact radius between indenter and material, R : radius of the spherical indenter. That is, the contact radius is estimated as the actual contact radius with careful consideration of material deformation behavior, such as pile-up and sink-in, around the indenter. For a power-law work hardening material, the material deformation behavior around the indenter is dependent on the work hardening coefficient (n) of material. And then, the true stress - true strain curve can be obtained based on the representative stress - representative strain relation and the estimated work hardening coefficient of material through the instrumented indentation technique (Fig. 2).
   
   

   

   Fig.2 Flow of true stress – strain curve determination through the instrumented indentation technique

   
   

1. ・For a power-law work hardening material, plasticity damage (ε_p) is also quantified approximately by the following equation;
   
   　　　　ε_p = n - n^n/n'

1. ・where, n : work hardening coefficient of virgin material, n' : work hardening coefficient of plastically-damaged material (Fig. 3). With work-hardening coefficient of virgin material, plastically-damage can be quantified through the proposed procedure by using the instrumented indentation technique.

   

   Fig.3 Schematic illustration of true stress – strain curve variation of power-law hardening material due to plasticity damage

   
   

1. ・The proposed procedure using instrumented indentation technique also has a big potential to be a useful tool for monitoring material embrittlement and degradation in in-service nuclear power plants or infrastructures.

1. ・The instrumented indentation technique, which has been used for material hardness test through the ages, can be applied to estimate residual stress through the method independent of material hardness.

1. ・Residual stress determination is essentially based on difference in indentation load at a certain level of indentation depth due to the existence of residual stress within material just below the indenter. The indentation load increases with the existence of compressive residual stress. Meanwhile, the indentation load decreases with the existence of tensile residual stress (Fig. 4).

   

   Fig.4 Difference in indentation load – depth curve due to existence of residual stress.

   
   

1. ・Non-equibiaxial residual stresses are separately estimated by using an asymmetric indenter, such as Knoop Indenter, with two different directions to same residual stress field. The difference in indentation load due to non-equibiaxial residual stress field, which is calculated by subtracting indentation load in stress free state from that in stress state, is influenced by direction of Knoop indenter to residual stress field (Fig. 5).
   
   
   
   

   

   Fig.5a Difference in indentation load – depth curve due to non-equibiaxial residual stress fields

   

   Fig.5b Procedure for residual stress measurement by using Vickers and Knoop indenters
   
   

1. ・Application of the conventional residual stress determination through the instrumented indentation technique was limited to only a few cases because it required the reference value of indentation load under non-stressed condition at every measurement location. In the newly-developed method, actual non-equibiaxial stresses on metal surface are obtained through the instrumented indentation technique by using Vickers and Knoop indenters without reference values of indentation load (or hardness) under non-stressed condition.

1. ・In the newly-developed method using Vickers and Knoop indenters, non-equibiaxial residual stresses σ_x and σ_y are estimated, respectively, by the following equations as;
   
   　　　 σ_x = {(L₂-ηL₃)(α_⊥-ηα_v)- (L₁-ηL₃)(α_//-ηα_v)}/{(α_//-ηα_v)²-(α_⊥-ηα_v) ²}
   　　　 σ_y = {(L₁-ηL₃)(α_⊥-ηα_v)- (L₂-ηL₃)(α_//-ηα_v)}/{(α_//-ηα_v)²-(α_⊥-ηα_v) ²}

1. ・where, L₁ : indentation load obtained by using the Knoop indenter (long diagonal is parallel to residual stress σ_x), L₂ : indentation load obtained by using the Knoop indenter (long diagonal is perpendicular to residual stress σ_x), L₃ : indentation load obtained by using the Vickers indenter, η : ratio of indentation load obtained by using Knoop indenter to that of Vickers indenter under non-stressed conditions, α_// : conversion factors determining the relation between residual stress and indentation load change due to residual stress (long diagonal of Knoop indenter is parallel to uniaxial stress), α_⊥ : conversion factors determining the relation between residual stress and indentation load change due to residual stress (long diagonal of Knoop indenter is perpendicular to uniaxial stress), α_v : conversion factors determining the relation between residual stress and indentation load change due to residual stress (for Vickers indenter). Based on continuous studies in future, material-dependent database of these factors (η, α_//, α_⊥ and α_v) can be available.

Phase 1 : Research and Development Phase

1. (1) Components:
   Nuclear power plants, Infrastructures, etc.

1. (2) Location:
   Material surfaces

1. (3) Materials:
   Steels, Metals, Hard materials

1. (4) Condition(Pressure,
   Temperatures, etc.) :
   Anywhere (depends on request)

1. ・Semi-nondestructive technique

1. ・Simple, compact and affordable device

1. ・In-service inspection

1. ・Material hardness-independent stress determination

1. ・True stress - true strain curve estimated by instrumented indentation technique is in good agreement with the tensile test result for structural steel (Fig. 6).

   

   Fig.6 Comparison of true stress – true strain curve between instrumented indentation technique and tensile test
   
   

1. ・Distribution of plastic strain around the notch in the tensile specimen estimated by instrumented indentation technique is in good agreement with those calculated by finite element analysis. (Fig. 7)

   

   Fig.7 Comparison of estimated and calculated distribution of plastic strain around the notch in tensile specimen at different strain levels
   
   

1. ・Residual stress measurement in carbon steel welds (Fig. 8)

   

   Fig.8 Comparison of measured residual stress distribution in carbon steel welds between instrumented indentation technique and X-ray diffraction method
   
   

1. ・Residual stress measurement in low carbon austenitic stainless steel welds (Fig. 9)

   

   Fig.9 Comparison of measured residual stress distribution in low carbon austenitic stainless steel welds between instrumented indentation technique, X-ray diffraction and stress relief methods

1. ・M. Miyabe, M. Iyota, S. Okano and M. Mochizuki, “Semi-destructive Method for Evaluation of Local Mechanical Properties in the Notch-Tip Region using an Instrumented Indentation Technique”, Quarterly Journal of the Japan Welding Society, Vol. 31, No. 4, 2013, pp. 114s-118s.
2. ・S. Okano, M. Miyabe and M. Mochizuki, “Semi-Nondestructive Determination of Anisotropic Stress-Strain Curve Using Asymmetric Indenters with Different Vertical Angles”, E-Journal of Advanced Maintenance, Vol. 7, No. 1, 2015, pp. 96-101.
3. ・S. Okano and M. Mochizuki, “Proposing a new semi-nondestructive measurement of non-equibiaxial residual stress field using indentation technique without reference value of hardness under non-stress state”, Transaction of the JSME, Vol. 80, No. 820, 2014, SMM0355. (in Japanese)
4. ・ D. Kanamaru, S. Okano and M. Mochizuki, “Semi-Nondestructive Measurement of Weld Residual Stress Field in Austenitic Stainless Steel using Indentation Technique without Reference Load under Non-Stress State”, E-Journal of Advanced Maintenance, Vol. 7, No. 1, 2015, pp. 14-19.

Japan Society of Maintenology (ejam@jsm.or.jp)