Using Microindentation for Measuring the Yield and Tensile Strength of Aluminum and Steel

The stress at which a material begins to deform plastically, and will not return to its original shape when the applied stress is removed, is known as the yield strength (YS). The maximum stress that a material can withstand while being pulled before breaking is the ultimate tensile strength (UTS). These two properties indicate the upper limit to the load that can be applied to mechanical parts and structure, and also play an important role in materials production including forging, pressing, rolling and annealing.

Importance of YS and UTS Measurement Using Indentation Technique

Traditionally, a tensile testing machine, a large instrument requiring enormous strength to pull apart the test specimen, is used to test the YS and UTS. To properly machine many test coupons for a material (since each sample can only be tested once), is both time-consuming and costly.

Noticeable variance in the test results can be caused by small defects in the sample. Furthermore, the different configuration and alignment of the tensile testers in the market often results in substantial variations in both the mechanics of testing and their outcomes.

Nanovea’s innovative indentation method provides YS and UTS values directly that are comparable to those measured by conventional tensile tests. This opens up a new realm of possibilities for all industries. The simple experimental setup significantly reduces the time and cost for sample preparation compared to the coupons with a complex shape for tensile tests.

It is possible to perform multiple measurements on one single sample thanks to the small indentation size. It can prevent defects in the tensile test coupons created during sample machining from influencing the results. Furthermore, it allows YS/UTS measurements on localized areas and small samples which is vital for YS/UTS mapping and local defect detection of auto structure or pipelines.

Indenter and depth sensor on the test sample.

Figure 1. Indenter and depth sensor on the test sample.

Measurement Objective

In this application, the YS and UTS of metal alloy samples including aluminum AI6061 and stainless steel SS304 are measured using the Nanovea Mechanical Tester in indentation mode. The test samples were chosen due to their commonly recognized UTS and YS values in order to show the reliability of the indentation method.

Measurement Principle

ASTM E2546 and ISO 14577 are the standards for instrumented indentation upon which nanoindentation is based. Nanoindentation uses an established method in which an indenter tip with a known geometry is driven into a specific site of the material to be tested. This is done by applying an increasing normal load.

When it reaches a pre-set maximum value, the normal load is reduced until complete relaxation occurs. A piezo actuator applies the load and it is measured in a controlled loop with a high sensitivity load cell. The position of the indenter relative to the sample surface is precisely monitored with high precision capacitive sensor during the experiment.

The load/displacement curves that are created as a result provide data specific to the mechanical nature of the material under examination. Established models are then used to calculate the quantitative modulus and hardness values for such data. Nanoindentation is especially suited to penetration depth and load measurements at nanomter scales because it has the following specifications:

  • Depth Resolution (Theoretical): 0.003 nm
  • Depth Resolution (Noise Level): 0.15 nm
  • Maximum Displacement (Dual Range): 50 mm or 250 mm
  • Load Resolution (Theoretical): 0.03 mN
  • Load Resolution (Noise Floor): 0.3 mN
  • Maximum Force: 400 mN

Analysis of Indentation Curve

Following the ASTM E2546 (ISO 14577), elastic modulus and hardness are determined through load/displacement curve for the below example.

Load-displacement curve of nanoindentation.

Figure 2. Load-displacement curve of nanoindentation.


The hardness is derived from the maximum load, Pmax, divided by the projected contact area, Ac:

Young’s Modulus

The reduced modulus, Er, is derived from:

This can be calculated having determined S and Ac from the indentation curve by using the area function, Ac being the projected contact area. The Young’s modulus can then be derived from:

Where Vi and Ei are the Young’s modulus and Poisson’s ratio of the indenter and V is the Poisson’s ration of the sample tested.

How are These Calculated?

A power-law fit through the upper 1/3 to ½ of the unloading data intersects the depth axis at ht. The slope of this line gives the stiffness, S. The contact depth, hc, can then be determined as:

The indenter area function is used to calculate the contact area Ac. This function depends on the diamond geometry and, at low loads, on an area correction.

The area function is Ac=24.5hc2 for perfect Berkovich and Vickers indenters. The area function is Ac=2.60hc2 for the Cube Corner indenter and Ac=2πRhc for a Spherical indenter, where R is the radius of the indenter. As previously mentioned, the elastic components can be modelled as springs of elastic constant E, given the formula: where E is the elastic modulus of the material, ε is the strain that occurs under given stress and σ is the stress. This is similar to Hooke’s Law. The viscous components can be modeled as dashpots so that the stress-strain rate relationship can be given as where η is the viscosity of the material, dε/dt is the time derivative of strain and σ is the stress.

Nanovea provides the tool to gather the data of displacement versus the depth during creep time because the analysis is highly dependent on the model that is chosen. The software gives the maximum depth of indent and the average speed of creep in nm/s. When loading is quicker, creep may be best studied. A spherical tip is a better choice.

Other Possible Measurements by Nanovea Mechanical Tester

Fatigue testing, Compression strength, Fracture Toughness, Stress-Strain & Yield Stress and many others.

Test Conditions and Procedures

The Nanovea Mechanical Tester performed the YS/UTS tests in Microindentation mode. A cylindrical flat diamond tip of 200 mm diameter was used. AI6061 and SS304 alloys were chosen for their commonly recognized YS and UTS values and their extensive industrial application.

This was to show the great potential and reliability of the indentation method. In order to avoid the influence of surface roughness or defects to the test results, the alloys were mechanically polished to a mirror-like surface prior to the tests. During the test depth versus load was recorded. Table 1 lists the test conditions. Over ten tests were performed on each sample in order to ensure the repeatability of the test values.

Table 1. Test conditions of YS & UTS for SS304 and Al6061.

Material SS304 Al6061
Applied Force (N) 40 30
Loading rate (N/min) 80 60
Unloading rate (N/min) 80 60

Results and Discussion

Figure 3 shows the load-displacement curves of the SS304 and AI6061 alloy samples with the flat indenter imprints on the test samples insert. A set of special algorithm developed by Nanovea analyses the “S” shape of the loading curve and the software automatically calculates the YS and UTS. These are summarized in Table 1 which also lists the YS and UTS values obtained by conventional tensile tests for comparison.

Load-displacement curves of SS304 and Al6061 samples. The flat indenter imprints on the test samples are inset.

Figure 3. Load-displacement curves of SS304 and Al6061 samples. The flat indenter imprints on the test samples are inset.

The results show that the values of the YS and UTS for the AI6061 and SS304 alloys measured using the tensile and indentation techniques are in good agreement. The UTS and YS tested by the Nanovea Mechanical Tester in indentation mode show superior precision and repeatability.

Table 2. YS and UTS of SS304 and Al6061 measured using indentation and tensile tests.

Material Yield strength (MPa) Ultimate tensile strength (MPa)
Indentation Tensile test Indentation Tensile test
SS304 277±21 275 609±16 620
Al6061 231±18 241 301±9 300

The YS and UTS evaluation in this study is substantially more cost- and time-effective than conventional tensile test procedure. It provides a solution of detecting localized mechanical defects of mechanical parts in service, does not require complicated sample machining, and enables fast quantitative mapping of YS and UTS values on small samples.


This application demonstrates the capacity of the Nanovea Mechanical Tester in evaluating UTS and YS of aluminum and stainless steel alloy sheet samples. This simple experimental design reduces cost and time for sample preparation required for tensile tests.

Small indentation size means that it is possible to perform multiple measurements on one single sample. This allows YS/UTS measurements on localized areas and small samples and provides a solution for YS/UTS mapping and detection of local defects of auto structure or pipelines.

The Nano, Micro or Macro modules of the Nanovea Mechanical Tester all include ASTM and ISO compliant scratch, wear and indentation tester models, providing the widest and most user friendly range of testing available in one single system. The unmatched range that Nanovea provides is an ideal solution for determining the full range of mechanical properties of soft or hard coatings, thin or thick, films and substrates, including hardness, adhesion, Young’s modulus, wear resistance fracture toughness, and many others.

Additionally, optional 3D non-contact profiler and AFM Module are available for high resolution 3D imaging of scratch, wear and indentation track as well as to other surface measurements such as roughness.


This information has been sourced, reviewed and adapted from materials provided by Nanovea.

For more information on this source, please visit Nanovea.


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