Nanoindentation Library

Classes to evaluate indentation data and indenter tip

Methods: iso, multiple unloading segments, csm
Vendor: Agilent, Hysitron, FischerScope, Micromaterials
Indenter tip: shape of indenter tip and gantry stiffness (that what you calibrate)

UNITS: one should use mSI units in this code, since Agilent area function is unit-dependent
[mN], [um], [GPa] (force, length, stress)

Variables: differentiate different length

array of full length: force, time, depth, validMask, … [used for plotting]
array of valid length: E,H,Ac,hc, … [only has the length where these values are valid]
force[validMask] = pMax
all these are vectors: OliverPharr et al methods are only vector functions

Bases: IndentationInputMixin, IndentationMainMixin, IndentationTheoryMixin, IndentationHertzMixin, IndentationPlotMixin, IndentationCalibrationMixin, IndentationVerificationMixin

Main class of indentation

Initialize indentation experiment data

Parameters:

fileName (str) – fileName to open (.xls, .hld)
nuMat (float) – material’s Poisson ratio.
tip (tip) – tip class to use; None=perfect
surface (dict) – dictionary describing the surface find
model (dict) – numerical parameters that determine the evaluation
output (dict) – links that describe the output (graphs and print-to-screen)

fillVendorDefaults() → None: fill defaults depending on vendor, if information is not yet present

class micromechanics.indentation.Tip(shape: Any = 'perfect', interpFunction: Callable[[ndarray], Any] | None = None, compliance: float = 0.0, plot: bool = False, verbose: int = 0)

Bases: object

The main class to define indenter shape and other default values.

__init__(shape: Any = 'perfect', interpFunction: Callable[[ndarray], Any] | None = None, compliance: float = 0.0, plot: bool = False, verbose: int = 0)

Initialize indenter shape

Parameters:

shape (list) – list of prefactors (default = “perfect”)
interpFunction (function) – tip-shape function Ac = f(hc), when it is given, other information is superseded
compliance (float) – additional compliance in test [um/mN] (sensible values: 0.0001..0.01)
plot (bool) – plot indenter shape
verbose (bool) – output

areaFunction(h: ndarray) → ndarray

AREA FUNCTION: from contact depth hc calculate area
analytical functions inside are using [nm]; the outside of this function uses [um]|br| hence at the start and end there is conversion. Interpolation functions use the outside units directly: contact depth [um] and projected area [um^2].

prefactors:

“iso” type area function A=ax^2+bx^1+cx^0.5…, [nm]

“perfect” type area function of a perfect Berkovich A=3*sqrt(3)*tan(65.27)^2 hc^2 = 24.494 hc^2

“sphere” type: A=pi(2Rh-h^2), h=depth, R indenter radius; for small h-> h^2=0
prefactors [-pi, 2piR], R in nm does not account for cone at top

Parameters:: h – contact depth in um

areaFunctionInverse(area: ndarray, hc0: ndarray | None = None) → ndarray | None

INVERSE AREA FUNCTION: from area calculate contact depth hc
using Newton iteration with initial guess contact depth hc0

prefactors:

“perfect” type area function uses the direct inverse of a perfect Berkovich tip
other monotonic area functions are inverted numerically

Parameters:

area (numpy.array) – projected contact area
hc0 (numpy.array) – initial Guess contact depth

Returns:

h = total penetration depth

Return type:

numpy.array

plotIndenterShape(maxDepth: float = 1, steps: int = 50, show: bool = True, tipLabel: str = 'this tip', fileName: str = '') → None

check indenter shape: plot shape function against perfect Berkovich
analytical: perfect shape is 2.792254*x

Parameters:

maxDepth (numpy.array) – maximum depth [um] to plot; default=10um
steps (int) – number of steps for plotting
show (bool) – show figure
tipLabel (str) – label for this tip
fileName (str) – if given, save to file

property prefactors: list[Any] | None

Backward-compatible representation of the tip area function.

Returns:: area-function prefactors followed by the shape name, or None for interpolation tips.
Return type:: list[Any] | None

setInterpolationFunction(interpFunction: Callable[[ndarray], Any]) → None

The interpolation of tip-shape function Ac = f(hc)

From Oliver-Pharr Method, projected area of contact Ac can be obtained by measuring contact depth hc.
When the interpolation function is given, other information is superseded.
The interpolation function takes contact depth in um and returns projected area in um^2.

Parameters:: interpFunction (function) – interpolation function from contact depth [um] to projected area [um^2].

Default Dictionaries

Default Model

Key	Default	Description
nuTip	0.07
modulusTip	1140	GPa from Oliver,Pharr Method paper
beta	0.75	beta: contact depth coefficient
nonMetal	1	switch between metal=0 and nonMetal=amorphous=default=1.
driftRate	0	drift rate in [um/s]
unloadPMax	0.99	upper end of fitting domain of unloading stiffness: Vendor-specific change
unloadPMin	0.5	lower end of fitting domain of unloading stiffness: Vendor-specific change
unloadInitialM	-1	initial value of m that is used to determine the initial values of B and hf, which are then used to fit the unloading curve. 1<m0<10, if -1 then best m0 is automatically identified
relForceRateNoise	0.02	threshold of dp/dt use to identify start of loading: Vendor-specific change
relForceRateNoiseFilter	‘median’
forceNoise	0.001	threshold force to identify start of loading
evaluateSAtMax	True	evaluate stiffness at maximum or at end of power-law fit domain
maxSizeFluctuations	10	maximum size of small fluctuations that are removed in identifyLoadHoldUnload
cropSlopeToLoading	True	crop the slope to the domain between the surface and loading, after those are identified

Vendor Dependent Defaults

Vendor	unloadPMax	unloadPMin	relForceRateNoise	Description
Agilent	0.999	0.5	0.02
Hysitron	0.95	0.4	0.2
Micromaterials	0.99	0.5	0.02
FischerScope	0.95	0.21	0.01
Hdf5	0.99	0.5	0.02
AgilentHDF5	0.99	0.5	0.02
KLAHDF5	0.99	0.5	0.007	enhanced accuracy
FischerScopeHDF5	0.99	0.21	0.02	reduced accuracy
MicromaterialsHDF5	0.99	0.5	0.02
HysitronHDF5	0.99	0.5	0.04
FemtotoolsHDF5	0.99	0.5	0.04
SurfaceHDF5	0.99	0.5	0.04

Default Output

Key	Default	Description
verbose	2	the higher, the more information printed: 2=default, 1=minimal, 0=print nothing
plotLoadHoldUnload	False	plot intermediate steps; helpful for debugging
ax	None	matplotlib axis to use for plotting
plotWithLabel	False	plot legend
progressBar	None	callback function to use for plotting progress bar f(value, location)
successTest	[]	list of all test with valid load-hold-unload sequence

Default Surface

Key	Default	Description
surfaceIdx	{}